Nowadays one finds books and online websites that help you to name babies. What are the earliest instances of these? I would assume that these would be in Europe, China or the Middle East, but if other geographies/cultures were using them, that would be acceptable too.
Down the ages, these mainly did not exist because, down the ages, most people were unable to read a book, and so couldn't use one.
Now, it has been suggested that the Bible was a baby-name book. However, a baby-name book (BNB) can be defined as one which exists for people to name their babies out of. I think both the Old and New Testament have a larger mission than that.
What you will find for most of history are that people know what their local onomasticon is; that is, the list of what's considered "a name" in the local culture. Ours is extremely free-wheeling and fond of borrowing and invention of mere sounds: don't take it as a model of most onomastica. That is why we want BNB so we can find something new and different.
In most cultures, people know their own onomasticon and can pick a name out of it without a book. They can also build new names pretty easily, if they like.
Take Anglo-Saxon. People had only one name, no regular use of eke-names, and to differentiate one Aethelwulf from another would start listing genealogy. Benno Seibs in Die Personennamen der Germanen [The Personal Names of the Germanic Peoples]. Wiesbaden: M. Sandig, 1970, lists all the roots and stems he could pull out of names of Teutons, Goths, Anglo-Saxons, Norse, &c. Anglo-Saxon parents would have these in their heads, both because they could cut and paste from all the names they had heard of, and because these were largely words in their language. Which didn't mean they could use anything. Some roots were male, some were female, and some were either. They knew which from common usage. They didn't need a book.
So the Hebrew people, in their earlier days, did not get their names by going through Torah and finding an old one. They built something.
Now, by 3rd C BC, they had the Hellenic habit of naming the first boy for his father's father, the second for his mother's father – and unlike Hellenes, they tried to get more, who would be named for other relatives. This becomes so engrained that, in the New Testament gospel of Luke, when Elizabeth/Elisabeth wishes to name her son John/Yochannen, everyone protests that none of the baby's relatives have that name. When her husband Zacharias backs up the choice, everone is just flabbergasted. So they weren't using any kind of book or list of names: it had to be a relative or benefactor (one reason "Alexander" became popular).
In Late Antiquity and the early Middle Ages, people didn't actually give a snap whether or not their name was "Christian." Those taking holy orders might take or be given a Latin name, but the use of those of established saints was a bit unusual, and certainly not required. These were the people establishing the list of saints' names: St. Patricius/Patrick, St. Hildegard, St. Ursula, and so on did not have an earlier saint of the name. When someone like Hrolf Ganger Christianized, he became Rollo, not in honour of a saint, but because that was the nearest Frankish/French name to Hrolf. All the Norsemen with him kept their Norse names, and he did, too, just not on the French rolls. You can track the cultural limits of Normandy by the place names that are based on some Viking name.
What did happen is that the names of some saints became popular for babies, and got repeated a lot. But people didn't pick them out of a Bible – laymen weren't supposed to have one. They just used what they knew of their onomasticon, whether that was Frankish or medieval French, Norman or English.
Over in Asia, they have more complicated names, but they still aren't picking baby names out of books. What they often do, is pick their own names when they are adults, or have it given by a near relative, but it's not off picklists. About the closest we get are Muslim names, where boys would be named abd-something, the something being one of the 99 titles of Allah. Starting with Abd-Allah, servant of the God. But there's Abd-al-Fattah, the servant of the Revealer, and ninety-some more.
The picklists first show up in Europe at the Reformation. Using a saint's name for your child was one way to mark it as not being in one of those Protestant groups that didn't believe in saints. Of course, a lot still did, like the Church of England. Even those Puritan names we all love, like Prudence, Temperance, Wait-still, and Conquer-all, were being invented, not picked off a list. Some Protestants, to name a baby, opened a Bible at random and blindly put down a finger. The first name as they ran down the column went to the baby. This meant babies got place names like Sharon or got one normally associated with the other sex, because many of these people couldn't read the surrounding text to get the context.
We start approaching the baby-name books in the 1600s when a few books record commonly known names, primarily for the benefit of law clerks, who had to be able to render them in Latin (1677, The Compleat Clerk, and so on.). However, Camden, in Remaines Concerning Britain (1605), gives us an entirely new attitude, a sense of history, and that the world will change. He records the names in common use, and such oddities as the minorities using family names as baptismal names, or giving children more than one baptismal name, for future ages who would not otherwise know what his culture did.
Before the 1800s, no one in European cultures much cared what their names "meant": names were names. A few might know because a line in the Bible remarks on it, but no one named a zillion single-birth sons Thomas/Tomás &c., because it meant "a twin." It was just one of the common names (and we're still using it as just a name).
But then came the 1800s, with the rise of philology and etymology as sciences. Etymologists originally would pick apart names because ancient words are buried in them that might not survive elsewhere. In many ancient and forgotten languages, the first words they could make out were the proper names. In some languages, like Visigothic, names are all we have left.
Other people found a bent for scholarship in digging out all the references to meanings of names in the Bible and classical authors. This is one reason the history of the etymology of names is so heavily based in Latin, Greek, and Hebrew. Books in this category include Moody (1863), Beleze in the same year, and Yonge (1884).
Combine this with a 19th century religious revival. Some people became terribly concerned that their friends had pagan names and poor little babies were being given names with no religious connotation at all. To correct this dreadful situation, they came out with baby-naming books for the first time. They decried naming little girls Rose or Aurora after mere things, when they could be Petronilla ("a little rock") or Ursula ("a small bear") after a saint. Others decried saints' names with ugly meanings, like "the blind one" or "quarrelsome," because surely the child would be influenced by it, even if no one ever told it what it meant (but Mom now knew and would be influenced in her reactions to every sty or assertion of independence).
The result of all this, along with a growing craving for novelty in naming, was the lists of What to Name the Baby. These became so popular that we find them among the miscellaneous articles and poems of The Rose of Deseret (1887, which claims Alexander is a Germanic name, rather than Greek) or in the back of a cookbook like Mrs. Clarke’s Cookery Book ... including ... What to Name the Baby (1883). They are with us today, and have the same characteristics – current versions of the names, current gendering of the names, lack of sources, and the insistence that every name have an etymological "meaning," correct or not. We have to guess that if they couldn't find someone's guess as to meaning, they simply omitted the name, because the phrase "meaning unknown" almost never appears.
This is about the same time for similar books in French and German.
LSS: No one had baby-name books until there were name-meaning books in the 1860s, and the BNBs followed them later in the 1800s. Notice how this coincides with the spread of literacy in the lower classes.
SOURCES (now you'll be sorry)(most of these are the old originals just so you can see when they appeared.)
anonymous. The Compleat Clerk, Containing the Best Forms of All Sorts of Presidents , For Conveyances and Assurances; And Other Instruments Now In Use and Practice. With the Forms of Bills, Pleadings and Answers In Chancery; As They Were Penned and Perfected by Eminent Lawyers, and Great Conveyancers, Both Ancient and Modern. Whereunto Are Added, Divers Presidents, Which Were Wanting: And Also Some Saxon Presidents; With the Exposition of Certain Words, Used in Ancient Charters: And the Proper Names of Men and Women: With Additions of Titles of Honour, Trades and Occupations, Cities, Counties, Bishopricks, Names of Offices, Months and Days; Numbers of Mony and Weights, in Latin and English: With a Computation of Years .. and so on. (1677)
Bardsley, Charles Wareing Endell. Curiousities of Puritan Nomenclature (1880)
Beleze, . Dictionnaire des Noms de Baptîsme [Dictionary of Baptismal Names] 1863
Camden, William. Remaines, concerning Britaine but especially England, and the inhabitants thereof their languages, names, surnames, allusions, anagrammes, armories, monies, empresses, apparell, artillarie, wise speeches, prouerbs, poesies, epitaphes (1605): London
Clarke, Anne. Mrs. Clarke's cookery book: comprising a collection of about fourteen hundred practical, useful and unique receipts : including " sick room cookery" and a number of excellent receipts entitled "The Doctor" : also what to name the baby, a complete dictionary of Christian names, their origin and signification; Toronto: the author; Baby Names, p. 375-385
Graff, J. J. Nederlandsche doopnamen, naar oorsprong en gebruik (1851)
Ingraham, Holly. Peoples' Names, McFarland (1997)
Larchey, Lorédan. Dictionnaire des noms contenant la recherche Étymologique des formes anciennes de 20,200 noms relevés sur les Annuaires de Paris (1880): Nancy: Maison Berger-Levrault & cie.
Long, Harry. Personal and Family Names (1883)
McCormick, Julian. The Child's Name: a Collection of Nearly Five Hundred Uncommon and Beautiful Names for Children; with an Introduction on the Tasteful Use of Christian Names. (1899) New York : W.H. Young
Muzaffereddin, Al-Hajj Shaikh. A Standard Dictionary of Muslim Names with 99 Names of Allah
Qazi, M. A. What’s in a Muslim Name.(1990). Chicago: Kazi Publication,
Siebs, Benno Eide. Die Personennamen der Germanen . Wiesbaden: M. Sandig, 1970. For Frankish, Saxon, Anglo-Saxon, and Norse names.
Spencer, Emily B.. The Rose of Deseret. (1887) Salt Lake City.
Yonge, Charlotte Mary. History of Christian Names (1884) London: Parker, Son, and Bourn.