The way I name my pets usually differs depending on the pet.
I named my Loque Lateralus, after the Tool song/album because I was on a Tool kick at the time I tamed him. I'd listened to my Tool playlist almost the entire time I was camping him, so it seemed fitting. Coincidentally, soon after taming him, I race changed my hunter and renamed her Aenima.
My Sambas is named Maneki after
Maneki Neko, because after camping him for a couple months and giving up, I got lucky on a fly-by after 4.2 came out.
My Deth'tilac is named Phobia. I'm terrified of spiders and was pretty disappointed when I saw that five of the new rares would be spiders. I stumbled upon him and originally went over there just to watch someone else tame him, but no one came. The longer I stared at him, the more I realized he's actually pretty cute for a bug. Naming him Phobia just seemed appropriate. ^_^;
When I tamed Ban'thalos, I actually had to stare at him for awhile before naming him. I ended up naming him Hikari, which is Japanese for "light". It finally clicked and I sat there wondering how it took me so long to come up with that. xD Naming my pets after Japanese words is actually my most common way of choosing a name, but it does differ depending on the pet.