I think you are perfectly right claiming that the Spanish or Portuguese form of a name may well be considered as "Latinate" in some way or other. In a dictionary you may find "imitative of or derived from Latin" as an definition of "Latinate" - and the Romanic languages are definitely "derived from Latin", as you explain so nicely. But I guess a lot of people who ask for the "Latinate form" of a name have something classical in mind.
In the case of Davidus the first half of the definition would apply, in fact I think DAVIDUS is rather an artificial name and we can be thankfull it didn't prevail. I would stick to DAVID
, in fact we called our boy DAVID
which I think is a lovely name (opinion board!).Andy