In Josephus' Against Apion (1:18) he writes in the name of Menander the Ephesian that Matgenus was one of the Tyrian kings, but I have seen other sources (like Wikipedia, et al.) refer to this king as Mattan. Why is he sometimes called Matgenus and sometimes called Mattan? Who decided that Matgenus means Mattan?
The main source for confusion is that different sources use different names for that certain person Matgenus (Μάτγηνος) / Mattan. He's said to be the father of Dido who founded Carthage. There are a lot of historians (greek, roman) who wrote about Dido, herself being a quite "popular" person, using different names for her father (Timaeus has "Mutto" (cf. Josephus, C.A. I:157: Μύττυνος); Justin: "Mutgo"; Servius: "Methres"; Virgil: "Belus"). Furthermore, there are problems regarding the tradition of Josephus' texts - there are medieval manuscripts in greek and armenian, with a wide range of variants.
So, everyone speaking about "Matgenus / Mattan" has to decide which source to follow and which tradition to prefer. Part of this decision is to think about possible mistakes by scribes who copied a manuscript. The difference between matgenos and mattenos in greek is just the difference between γ and τ (which may look quite similar in handwritings).
Someone believing that mutgo is the correct name for "Matgenus / Mattan" would prefer the latinised version "Matgenus" when editing Contra Apionem. Someone else may stick to a certain manuscript, keeping Mettenos / Mattenos (cf. Thackeray in the Loeb edition, p. 212/213; also Niese in the Weidmann edition).
According to Siegert, "Flavius Josephus - Über die Ursprünglichkeit des Judentums (Contra Apionem)", only Codex S (Codex Schleusingensis, a greek codex dating before 1544) has Μάτγηνος instead of Μέττηνος. Since the greek editio princeps (Arlenius, Basel 1544) is based on Codex S, it's very likely to be the source for that version. Interestingly, it's again Codex S at I:157 with Μύτγονος instead of Μύττυνος!
The usual form of the name in English is Mattan, which is found both in the Bible and in Herodotus where the name is spelled Ματτην. This transliteration is, in my opinion, misleading, but it is very common. In my opinion eta should be tranliterated in most cases into English as "ai", thus it should be Mattain. Unfortunately, many scholars translate both alpha and eta as "a", or sometimes tranliterate eta as "e", which I find to be very misleading. Many other Greek words suffer from similar misleading transliterations, which are in my view more or less incorrect. For example the letter upsilon which sounds like "oo" is usually transliterated in English as "y", which is completely misleading.
In Assyrian inscriptions the name is spelled Mittena. The "e" in this transliteration should be sounded as a long "a" ("ay" or "ai"), thus, it is essentially the same as the Greek version of Herodotus.
In Against Apion, Josephus writes the name as Μεττηνος, which is essentially exactly the same as Herodotus spells it. The Anglicization to "Matgenus" was possibly due to the translation of the 18th-century theological fanatic William Whiston who is not known for his linguistic accuracy.