Well, normally I only capture rares and I immediately rename them with their original name. I have only gotten two mobs that didn't have their original names. 1 is a Scorpid I caught to see if Scorpids were as good as everyone said. If I recall correctly I named him Draci. The name just randomly came to me.
The story of my current mount is kind of interesting, at least I think so. He is Stanley from Feralas and he was a pain to keep. I pretty easily caught him but didn't have the correct food for him at the time so I was in a rush to get back. Had 2 fish and that just barely got him into the yellow. On the way back we ran into a rogue 2 levels higher than me and I couldn't avoid the fight. I won, largely because I know how to handle rogues now and, at the time, had alot of trinkets and stealth detection from engineering. In the process though my Stanley died. At this point I hadn't renamed him.
Well, I watch my hearth refresh and opt to go back to org. This entire time I haven't raised him yet and when I get back to Org I wait until I am back at the stable to raise him. It says I am not able to so I think maybe he somehow revived himself and checked the stable. He was in there listed as my main. I quickly hit the whistle and proceed to see Draci instead of 'Wolf' as he is blandly listed. Well, for a good 2 days I didn't do anything. I spent the entire time watching GM's temporarily give him back to me only to do his little phase trick and then disappear again not allowing me to keep him. Finally, after alot of frustration on 'Jonas' part (the GM helping me), we finally get 'Wolf' back permenately. Well, because I had to deal with him phasing in and out of reality, I decided to name him Phase.
Anyways, to make a long story short, me and Phase have been together for awhile now and I love the look of him. I can't see myself replacing him now because of all the hard work it took to get him.