Who came up with the name "Peloponnesian War"?

Question

If I understand correctly, Thucydides actually called his book just History. If that is correct, then at what point did it become known as History of the Peloponnesian War?

EDIT: Here is how he begins:

Thucydides, an Athenian, wrote the history of the war between the Peloponnesians and the Athenians, beginning at the moment that it broke out, and believing that it would be a great war, and more worthy of relation than any that had preceded it.

EDIT 2:

Come to think of, I ran a search on the Perseus website (it's great we have it!) and it turns out Thucydides did use the term once:

The Median war, the greatest achievement of past times, yet found a speedy decision in two actions by sea and two by land. The Peloponnesian war was prolonged to an immense length, and long as it was it was short without parallel for the misfortunes that it brought upon Hellas.

Still, I think it is not obvious that this term should have become the title of the whole book. Or am I missing something obvious here?

Answer 1

According to http://www.historyofinformation.com/, the first Latin translation was commissioned by Pope Nicholas V and completed in 1452 by Lorenzo Valla. The image below is from the first page of the first book. My Latin is below basic, but the first line seems interesting, a specific reference to 'Peloponnesian War'.

Answer 2

I am unsure if this is the first mention of Thucydides' 'history of the Peloponnesian war' but this is Thomas Hobbes' first sentence, thirteenth paragraph of the section titled 'On the life and history of Thucydides' from "History of the Peloponnesian War, Thomas Hobbes, Ed." It comes from the 1843 translation of his 1628 version.

    To this I say, that it was the duty of him that had undertaken to write
    the history of the Peloponnesian war, to begin his narration no further
    off than at the causes of the same, whether the Grecians were then
    in good or in evil estate.

Here is the link.