I just like whatever sounds good. Which is basically any name that I didn't make up. I'm horrible at naming things xD I don't mind character names, especially if they're unusual or I've never heard of them, and some people have really awesome ones that they just made up. I tend to make up random phrases when I'm naming.
I like real world names, adjectives and country names for my pets.
I personally named my pets after various things that I like. I don't like making up names out of nothing.

I like RL names or RL words that fit with my pet.

His name is Edgey (which of course is my username). It just fits cause he's evil. Plus that's what his personality is like, Edgey.

Virosan. I named him that cause it sounded like a good vampire bat name.

Leishen. I dunno why or where theis came from, but I liked the name.
I have 6 other pets... but I'm not gonna put them up here.
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Under 15 words, easily pronounced, first letter is caps, and it has no numbers.
Lol for me a cool name would be:
Banner by Yiri; OC fanart by by V i s u a l R o c k e r (Gaia) CosplayHAs Saving up for royalty - 26/28 crowns
You. Have. Balthier. D: My god I envy you so much.
Um, anyways. I prefer actual names and words myself... I don't mind slapping on last names, either. My favorite of my pet's names is Zelinda, actually. The name of a minor planet and of a character in what's basically the old Italian "version" of Beauty and the Beast. owo
Simple, or related to the pet, no numbers or underscores. And the first letter must be capitalized. :c
Names like these make my eyes bleed:
Betty47347309
KawaiiNekoChanSama
sparkly_girlie__
Rfjrdgjlesraergfsdiwipjk
MrsEdwardCullenRose
. . . and any combination of that crap.
So as long as your pet isn't named like that, I probably approve. (Not that my approval matters--they're your pets and you can do whatever the hell you want with 'em. :P)
[sub]Of course, all of the above complaints can be dismissed if the name is handled as a well-played gag.[/sub]
Same here. D: Like the names of my own pets suggest, I prefer real names like those that may be the same as a character from a book/movie/TV show that I like (such as Rodney and Cam). I don't really like verbs, adjectives or random nouns, with the exception of places (such as Juneau, and Ghent, though he's actually named after a book character and not the place). Not that there's anything wrong with them, they just don't work for me when I try to make characters. :3
I also look at proper capitalization, and I don't even really like spaces in names. I like single word names, the shorter the better unless it's a really decent or nice sounding name. I don't like using punctuation, or variations of real word names either. If I can't get the name as is then I just find another. Again though, just a personal preference. :3 Aside from ones like said, there really aren't any names I hate. Unless I randomly associate it with something I hate. Without even a practical reason, I'd intensely dislike a pet named Spider, or Arachnid, for example. Two guesses why. :x
[edit] Whoa... Lol, I totally just realized that you changed your name . Nice pick.
I like names of characters, generally. I haven't gotten into RP or anything like that (not yet, at least), so I don't need to worry about limitations, or designing personalities for them. Also, it makes me feel like I have a little bit of that story/character for my own, which is nice. :)
Besides that, I also like some real-world names, but generally, I'll go for fantasy-sounding names that flow well, and sound cool/beautiful. I also have a big thing for proper capitalization, and numbers in the name = no, unless they're part of the name in the first place.
THIS. Hahaha, I laughed so hard.
I tend to like either made-up names, as long as they don't make your head hurt thinking about pronunciation, or real human names.
I like words that mean something to me or my personal opinions. Usually I would prefer capitalised but for some I like it not to be depending on the word and why I chose it.
I totally agree with Azzie about those dodgy names. =D
I like my pets names to have something to do with either the way they look, colour or personality :) For example, my Voodoo was named that because of her insane personality and Believe's name is linked up with her story :)
As said, names with a huge amount of numbers and wapanese text make me want to rip my eyes out and bury them in the garden ^_^ xD
LOL. There's so many pets in the pound with those fake japanese names. It's kind of sad.
For me pet names are pretty easy. My very favorite pet names are real word names that I somehow connect personally too. All of my pets meet that description. In some cases two word names work for me too... like Full Moon.
Real names like Corey, Bridgette stuff like that in "some" cases works for me most of the time not though unless the name is very special to me.
Any name that is not a real word though doesn't make the cut for me. Fake japanese names etc... I really dislike them.
Although when forced to be creative because other names are taken made up words with pizaz are enjoyable too. Like on neopets I made Quarkant and I'm pretty fond of that name. It makes me think of someones Quirks and that specific pet it super goofy with glasses and silly looking with a superman cape :)
Thinking about it, the only thing I require in a name is for it to be capitalised and to have no numbers in it. Beyond that, anything goes, though I prefer made up names to real words/actual characters. Even though I don't do much with my pets, I like them to be as blank as possible when I create them so I can do what I want (Lucemon highlights this perfectly. Still like the pet/name but from the start I knew if he was anything other than an Angelic -something- then it would bug the hell out of me). I also find it easier to get attached to made up names
Lol @ the wapanese! xD
Personally, I love rare names that have a good ring on them, as well as names that actually mean something. For example my lovely little Merle (GY fester) got his name when I tried to think something what actually has something to do with birds. "Little blackbird" is the meaning, but it's an actual name too. Thinking up names for characters (this includes pets as well, of course), going through latin names of flowers ,for example, is a good way to pick up a name. Many flowers symbolise something, and great names can be found via that way.
Also, I like made up-names, those bunches of letters that really don't mean anything but sound amazing. What could be taken as a real name, but they really aren't.
But of course, the most important things should be that the name is capitalised (first letter) and there's no anything.. what doesn't belong there. No one likes numbers in their names, me neither.
for me, it's real names. all of my pets have real names - even bandhu is an indian name, which fits with his character.
i also think that real word names are nice, but they are difficult to pull off, and must suit the pet and its personality. AND first letters must be capitalized, and everything must be spelt correctly.
/is picky