In Latin, how would you say something like
The boy’s name was Gaius.
I was thinking of using nomen, as we do in English
Nomen pueri Gaius erat.
I know some languages use the verb ‘to call’ in order to say ‘named’, but I wasn’t sure if Latin did this. While we’re on the subject, I am not sure if my cases are correct either.
That’s a fine translation, though more commonly you’ll find that Latin likes to use the dative case with names, so nomen puero erat Gaius would be just as good. And also, for instance, mihi nomen est Lucus, and I have a sister named Maia, so I could say meae sorori nomen Maia est; you get the idea.
You can also use the verb appellāre, i believe. I’m really tired right now, so I may be wrong.
my name is Jon(Ion, -is) = meum nomen est Ion/mihi nomen est Ion, as Lucus pointed out.
or i think you could say
me appello Ionem. I’m not sure about it, though. maybe “Ion” is n’t supposed to be in the acc. or maybe “appellare” doesn’t really mean “to call”, but I’m sure it’s at least close.
someone tell me if I’m wrong, amabo te.
… I’d just stick with what Lucus said. He’s right.
I suppose you could say it with appello, but the many idioms using nomen are the most common ways. If you were to say “I am called”, you would probably use the passive (appellor) rather than a reflexive, which is basically a Romance construction right down to the verb used. The “nomen (+dat) est ___” that Lucus gave is safe, and very nice because you can give the name by its nominative (which is important for purposes of declension). By all means, feel free to choose your own name, but I would go for the more Latinate Iohannes, -is 
Iohannes would be good, thanks. I think I read somewhere that Jonathan comes from the Hebrew word for “God has given” or something like that. So would I be horribly wrong in assuming that a fairly accurate translation would be Deudeditus? just wondering… 
It’s not easy to translate names by their meanings, which is why they are usually just transliterated. I see what you did now adding to “Deo dedit” a 2nd declension nominative ending. Adding declension endings to conjugated verbs is not the traditional way of creating names, but no one can tell you what your name is! Just look at “Benissimus” 
I thought your name was from “Deo deditus”.
Sorry for bugging again, but
Adding declension endings to conjugated verbs is not the traditional way of creating names…
What is the traditional way of creating names?
aaand…
Is Deo what one calls God (as in, "the God of Abraham)? I thought the word for God was Deus, or does that refer to a god within the “pagan” pantheon? just wondering… still new.
Names are very unusual in formation are not regularized. For this reason, I couldn’t tell you how to form a name with a given intended meaning if it didn’t already exist in Latin. Adding case endings to finite verb forms was never done, as far as I know. I am sure there is a lot of literature on the subject, Palmer’s ‘The Latin Language’ certainly discuss person/place name origins.
aaand…
Is > Deo > what one calls God (as in, "the God of Abraham)? I thought the word for God was Deus, or does that refer to a god within the “pagan” pantheon? just wondering… still new. >
deo is the ablative (or stem) of deus, which can refer to “a god” or later, “God”. Compound words where the first part is a noun usually just use the noun stem (e.g. deo) or a generic ‘-i’ ending (e.g. dei) for the first word of the compound. I don’t think the nominative (e.g. deus) would be used in the first part of a compound, even in a name.
Thanks! Haha! Deodetitus it is, I guess, since I’ve already become attached to it. quid in nomen est?
You’re not the only one.. In my early days I mistakenly though the gender of ars was masculine, hence my moniker of arslongus, instead of arslonga…
oh well, vive et disce!
Just look at “Benissimus”
I donno, your name always made perfect sense to me, maybe because “benissimo” is frequently used in Italian. It usually refers to very good food. 
Just to answer the other half of your original question: in Spanish they say “me llamo Colin,” i.e. “I call myself Colin” most of the time instead of “mi nombre es Colin” (“my name is Colin.”) While grammatically you could correctly do the same in Latin; I’m not sure if it’s the way they did it. (And all that’s discussed above.)
Latin’s tradition in appellation differs from that of the Romance languages. “I call myself,” is the modern pattern, or “I am called.”. But Latin had a ‘dative of possession,’ which was very handy; meaning that a Roman would say, “the name to me is Luke,” for example. It seems frightfully awkward in English, now that I write it out, but it just feels like second nature in Latin.
Latin’s tradition in appellation differs from that of the Romance languages. “I call myself,” is the modern pattern, or “I am called.”. But Latin had a ‘dative of possession,’ which was very handy; meaning that a Roman would say, “the name to me is Luke,” for example. It seems frightfully awkward in English, now that I write it out, but it just feels like second nature in Latin.
The dative of possesssion is not unknown to Romance languages, though it is not used in connection with names. Compare French:
Ces gants ne sont pas à moi - ‘These gloves are not to me’ = These gloves are not mine.
Cette montre est à elle = ‘This watch is to her’ = This watch is hers.
This construction has similarities with:
Nomen ei est Marcus - The name to him is M. = His name is M..
Come to think of it, is the possessive dative only used with names in Latin or can it be used in the French way too?
Yes, it be used for other things, too.
As a side note to this conversation, according to Bennett:
Here’s another option that I’ve come across a lot in the Aeneid:
Sum patria ex Ithaca, comes infelicis Ulixi,
nomine Achaemenides…
(III.613-614)
[I am from the homeland of Ithaca, a companion of unlucky Ulysses,
Achaemenides by name.]
So I could perhaps say, David nomine sum, though it might have a bit of an archaic feel.
-David