Names are considered in the application process. It's just one of many things that get checked and, like anything else, can be overlooked. Also, it depends heavily on which reviewer goes over your app. Some of us are strict, some are not, so it's just the luck of the draw in a lot of cases. Repeatedly submitting the same app, in the hopes that you'll get an easy immortal is something we like to call 'imm-fishing' and is not looked highly on.
Immortal names are expressly forbidden. Occasionally some immortal nicknames (San, Hal, etc.) will slip through as names or keywords, and we'll often remove these once we find them.
The names of existing characters are perfectly fair game. However, expect bad things to happen if it becomes obvious that you're trying to make a clone of an existing character.
Fantasy names are sometimes okay. If it's an obscure name, or somehow fitting, it'll probably get through. It typically only becomes a problem when the name is so common that it's very jarring, or when people try to make the character, not just the name.
That I've seen, fantasy names are usually only picked by new players, and most staff members are more lenient with them. Most experienced arm players tend to pride themselves on their originality, so instead of gruff dwarves named Thorin, we see a lot of 'macilent, crepuscular-eyed bipeds' as players try and dig up the most obscure terms they can find to make their characters.
Naephet