Actually, yeah, I'm going through a bit of this now in fact. Gonna get a bit lengthy here, apologies.
My one and only wolf for the longest time(and my go-to pet for everything) is a tamed Thunderlord Dire Wolf out in Blade's Edge who I named Umbergore. I think my love for his skin came from camping Barnabus back around mid-Wrath - after waiting on him all day, anxiously pacing back and forth on my dinky little ground mount I had him stolen from me in a massive show of asshattery by a blood elf hunter, who then tricked me into dueling and killed me with my own wolf. I wasn't really very knowledgeable at that point, and even though my level-capped guildies came out to teach him a lesson I didn't really get over the loss of what I thought should have been my dog - until Outlands, at least.
Funnily enough, despite him being my favorite pet I don't have any screenshots of me now that aren't of his butt. Have a screenshot of the PTR instead - just pretend I'm an orc, hah:
I love him and everything about him, something about his model and his animations just struck me as a grumpy old man sort - and after a faction change and many many hours of leveling, who wouldn't be old and grumpy? He's had a huge impact on my roleplay, but in theory he's getting pretty far on in years and, really, I'm kind of tired of looking at the same wolf all day. He doesn't even fight anymore ICly - he's at home, playing babysitter for Vee's daughter and her moderately annoying worg pup.
Figuring I'd just say he died during the Shattering, I let him go once before, and when the realization finally struck me I dropped everything to petition a GM for his return. He was only gone for a few days, but it still felt like I had lost a close friend. And yet he stayed in my main roster for weeks before taking his spot back in my stables, and I look at him for a long time every time I clean them out. It's not that I don't love him anymore, obviously, since I asked someone to restore him, but I just don't feel as attached to him as I used to be. He still sees his fair share of dungeons and he proved useful on the PTR(during Ulduar, where everyone either had a cat or a spirit beast, hah), but I wonder if it's time for a change all the same.
I've decided to adopt Caboodle's wolf Lemmy and see if he gets on any better with Veeka, and so far I really love the black coyote skin, but I just can't bring myself to let Umbergore go. For now, he's staying tucked away in my stables. Maybe another faction change back to my old Draenei self and a clean slate will make him more attractive again, or maybe it'll give me the will to let him go and say he's finally passed on. He's served me well through many a level and haphazard oldschool raid PuG, so in a way just talking about it makes me feel like I'm losing my real life dog. This is all absurd of course, since he's just pixels, but it's a little jarring to know that I'm thinking about getting rid of
my blob of reddish brown pixels. :P