It is very often that people get confused between a Latin version and a Spanish form, when it is, obviously, not the same thing. I guess it happens, among Spanish speakers more frequently, because of the common knowledge that Spanish comes from Latin. Never the less it is incorrect to think of Spanish as THE Latin version. Italian comes from Latin, Portuguese comes from Latin, even English has got lots of Latin in it, as everyone knows. There is also roots from Greek and Etruscan in Spanish, but no one assumes that the Latin form of Anthony is Anatolius, for some weird reason... (:op)
Any way, I just wanted to add that it is valid to think of a Spanish form of a name, when thinking of a Latin version (or any other of the Romance languages for that matter) because Latin is a dead tongue, The Romance languages are the transformed version of Latin and it is not so common any more, for someone to be named "DAVIDUS" (as Andy so kindly provided us with), now days. So, if someone wants to know of the "latinate form of..." it is valid to think of the Portuguese version, the Italian version and the Spanish version, although it is not the most accurate answer to the question. You where right to emphasis on the fact that you did not ask for any Spanish version, Anthony. It is not that "all of you forget the spanish form to Anthony, which is Antonio". And, "Of course, David is the only form, there is no other name", is an incorrect statement.
I don't mean to disregard Profe Estaban's theory, although his answer does surprise me, as he claims to be a professor... Oh well, too long for JMHO, but it is JMHO.