My favorite would probably have to be Silver. Crystal was my favorite game in the series for like a decade, and I absolutely adore HeartGold and SoulSilver as well. Silver and Blue were the only rivals who were sort of antagonistic in demeanor for a long while. His backstory of being Giovanni's son and the neglect leading him to act out and become a criminal himself, stealing his starter from Professor Elm's lab, made him pretty interesting compared to a lot of the other rivals throughout the series. Seeing him learn to care for his Pok?mon as the game progressed was pretty nice to see as well. Finally, probably the least important aspect, I also just like his character design on a base level.
Blue's my second favorite since he was the first and is pretty accomplished in his own right, becoming the Indigo League's Champion for a short time and then becoming the final Gym Leader of Kanto. It was good to see him and Red show up in Alola for that Battle Tree.
I've never really considered N to be a true "rival" since we had Cheren and Bianca, say whatever one will about them, though I can see why he would be considered one. I'd include him in honorable mentions next to Gladion, I guess.
Haven't fully gotten through my playthrough of Sword as of yet, so can't really speak to how much I like Bede, Hop, and Marnie overall. Bede's personality is fun, but his monotype Psychic team thus far has been underwhelming to defeat over and over again. Hop is decent, and I've not personally seen enough of Marnie to really for much of an opinion. Having seen a few spoilers though, I reckon that she might be able to make it to honorable mentions with N and Gladion by the time I actually finish the game.
Silver, first off. My young self named him a bad word for being a thief and abusive to his Pokemon. I thought he was a great rival because every time I ran into him it was a challenge and he eventually learned that if he treated his Pokemon with compassion it would bring out their true potential.
Second, N. It’s been a while since I played BW so I had to make sure he was who I thought I remembered. I don’t really remember why I liked him so much but he’s really the only one I remember besides Gary and Silver (and Wally but eh, it’s Wally) so he must’ve been a good rival.
I also chose Marnie because I really love SWSH and Hop/Bede are just annoying in my opinion.
Brendan because he's from Gen 3 and I always really liked his character while I played Sapphire. It's too bad he didn't show up in the anime at all. May is pretty good but I like Brendan more.
Barry.... actually I don't really know. It's been a long time since I played Pearl. I really love his character design though, super adorable!!!
And I picked Bede because from what I've seen in SwSh gameplay, he and Opal make me laugh. His hair is weird as heck tho lol