, thus why would he want to just give out his name to some clearly evil random guy trying to kill him and that's the first thing he tries to get out of gajeel
You know, you say that but i don't remember Gaajel being so cautious against someone that he would even hesisitate to say his name.
And again, is just his name, he can't assume that Ley would anything just by knowing his name, even if he is evil.
And is not like Ley gonna be on the nose about needing to know Gajeel name, like "Hey, tell me your name NOW" since:
Even if he not stupid (Well, he is stupid sometimes), Ley is way smarter than him, and there's severals ways to trick someone into saying they names to you.
Like, considering how hot tempered he is, Ley could just perster him with a weird nickname until he snaps and be like "Hey, my name is Gaajel Redfox you brat" or something
Ley could also use that one trick that is like, you say that you recognize the guy, then say a name complet different to them, so then can correct by saying they actual name like "oh, i know you, you the uhhh ah [Insert name here] right?" "What? I don't know who you talking about, my name is Gaajel Redfox"
Or the use the classic one, of introducing yourself first and asking they names. Considering how Gaajel likes to gloat about how he is the strongest dragon slayer, it could go something like this:
"Sin Archbishop of the Witch Cult representing Glutony, Rai Batenkaitos. What's your name?"
"...The Iron Dragon Slayer of Fairy Tail, Gajeel Redfox" or "The strongest Dragon Slayer, Gajeel Redfox"
The last one is a maybe, since i don't remember if Gajeel is the type to be like "Why should i give my name to someone who about to die" or something, but the other two should work.