Rangers and druids can have god only knows what weird animal companions, but everyone has a horse.  And they're completely interchangeable sets of numbers, all equally fast or smart or mean tempered.  The only difference is pure role-play.  So use your imagination, make something up if you haven't already,  and tell us about the most overlooked member of your party.

My human paladin has an absolutely massive (18 hands or 6 feet tall) blue roan percheron stallion named Gunpowder.  He is a curious, fun-loving goof who doesn't realize how big he is.  Once or twice, he's restrained prisoners by sitting on them.

My ranger has a pretty big draft horse named Gidget. Its honestly kind of stupid and keeps getting in the weirdest trouble.

One time we had to tender to port so different party members hopped on different tendering boats. Me, my horse, and our cleric got on one boat and as everyone was getting closer to the dock we noticed it was under attack by sahuagin. we get into a ranged battle with them but a few dive into the water and make their way into our boats. Eventually one hops on right behind Gidget and so I ask the DM, "I know I don't really have the ability to command or talk to animals yet but I'm sure we can all agree if something jumped behind a horse and it couldn't flee, it would kick the crap out of them.. right?" 

So the DM says sure, as long as it rolls high enough the horse would instinctively kick this sahuagin. Nat 20. Critical hit. Not only kicks the little turd out of the boat but kills it too.

My sorcerer's horse is named Hammerhoof.  I got him from a bandit who didn't need him any more and earned his name when I rode down one of his companions.  He's pretty much just a plain old horse, nothing special about him, other than he has a name and I am pretty sure the other horses in the party do not.

horse? pft, my kid's dwarf has a fangjaw boar named Snotty...he occasionally looses control of it on a failed animal handling check as it runs off to dig up a truffle.  he makes decent money off of those though.

In my current campaign I'm playing as a Goblin, and he actually rides a goat named Thaco. He's a bard, and Thaco is his performing companion, dancing along to the music he plays on his Squeezebox and accepting tips in her saddlebags. He uses the Speak with Animals spell to talk with her and plan out dance routines and the like, and she's a bit of a diva. He was kind of an outsider to his goblin tribe partly because he had a soft spot for animals, and he ran away to rescue Thaco from being killed and eaten by the rest of the tribe members who 100% wouldn't care how good of a dancer a goat is and would just see her as a source of meat.

Quote from TransmorpherDDS >>

In my current campaign I'm playing as a Goblin, and he actually rides a goat named Thaco. He's a bard, and Thaco is his performing companion, dancing along to the music he plays on his Squeezebox and accepting tips in her saddlebags. He uses the Speak with Animals spell to talk with her and plan out dance routines and the like, and she's a bit of a diva. He was kind of an outsider to his goblin tribe partly because he had a soft spot for animals, and he ran away to rescue Thaco from being killed and eaten by the rest of the tribe members who 100% wouldn't care how good of a dancer a goat is and would just see her as a source of meat.

 My warlock in my other campaign's familiar owl is named Thaco lol

Nobody in my group got the joke... which is odd because I'm actually newer to D&D than most of them... I've just heard a lot of stories.

My current DM and I played 2e together in the army years and years ago.  He complains about the old THAC0 system all the time.  I figured it would be a great name for my familiar.  I think the rest of my current group got their start in 3.5.

Ohhh I wish I could remember what my mom named the party's horse, back when I was DMing... I let my players get hold of a horse and small wagon pretty early on, and they had a couple of retainers who they'd roleplayed their way into gaining the loyalty of, so they had a pretty nice set-up for traveling and that was purely a reward for getting into the game and getting into character. And my mom had obliged me, when we were down a player, by joining the group,  and her first priority was naming the horse.

It was something very cute, that's all I remember. He was purely a carthorse, no one rode him into combat. When the gang went dungeon diving, if the wagon wasn't going to be able to make the journey for whatever reason, then the retainers would wait and guard camp and the horse would stay with them. But the players did get attached to him as a group. The party also made a point of decorating the wagon, partway through. So our horse became a very distinctive sight whenever they rolled into town, and I was never mean enough to have something attack him.

Is this in a Norse Campaign? If so, is your name Odin?

Norse MYthology!

The horse Cadenza rides is named Vivace (vih - vah - chee).  She is a beautiful cream colored riding horse with a blonde mane and tail.  She is somewhat aware of her natural beauty and tends to prance a little when she is around people and not galloping.  She also instinctively knows she belong to Cadenza so she is believed to be temperamental and high strung, but it is only that she is nervous around anyone else.

Cadenza realizes she is a rare animal and treats her very well, leaving her to graze on grass only rarely.  So in addition to carrying feed for Vivace when he travels, he brings fruit like apples and pears as well to spoil her.  He has also spent some money on obtaining fine leathers for her dyed a medium brown to compliment her color, mane and tail.  Her halter is dyed red, pale and brown with a beautiful concho of a lute in the center.  Her bridle is braided, saddle softened and supple and the saddlebags have beautifully tooled finish of scenes of tranquil forests with pixies and dryads dancing next to a cool stream.  She is the very picture of beauty and health and Cadenza expects her to live many years sharing in his adventures.

Sounds a million times better than my mule, Largo (lar-go, though large-o was appropriate, too). Nothing bothered him because he didn't bother to do anything.🤣