Honestly, even I wasn't sure how or where I found MyRolePlay for Vanilla since, seemingly, it only came into existence around the time of The Burning Crusade (retail). Regardless, here's two dedicated links for the world's most perfect profile RP addon. And also, two other ones people liked.
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MyRolePlay (v2.2.2, v2.2.3)
Add a detailed profile to your character and see other characters' profiles in WoW's tooltips.
(AddOn automatically adds your character to "xtensionxtooltip2" and "MyRolePlay" chat channels, which is how it communicates.)
Change Log
flagRSP and FriendList
Add a simple profile to your character, see others' profiles in pop-up tooltips, and keep a database of roleplayers.
(AddOn automatically adds your character to "xtensionxtooltip2" chat channel, which is how it communicates.)
ImmersionRP (Alpha 2 or Alpha 3 only)
Add a simple profile to your character and see others' profiles in pop-up tooltips.
(AddOn automatically adds your character to "xtensionxtooltip2" chat channel, which is how it communicates.
Additionally, ImmersionRP can be set to add your character to "immersioncomm", instead.)
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Personally, I recommend MyRolePlay. It has the most options for profiles, such as renaming your character entirely (for you and other MRP users) and maintains full compatibility with flagRSP while offering a pleasing, non-intrusive interface with logical button placement and a few options for customizing tooltips and the like.
If flagRSP2 or ImmersionRP Alpha 4 were available for Vanilla, I would probably be less biased because those versions of the linked AddOns actually have much of the same options. ImmersionRP, in particular, seems to be the complete underdog, here, as the "immersioncomm" channel is frequently abandoned. Of course, that's an optional function, so…
Anyway, MyRolePlay seems the most compatible and most capable across the board – not to mention the least intrusive. (Pop-up profiles? Really?) But again, I'm wholeheartedly biased since the other available RP profile mods aren't as up-to-date as MyRolePlay. That, and I've been using it since at least The Burning Crusade retail. Heh.
06/07/2022 Edit:
I just found out something interesting about this version of MyRolePlay.
It doesn't support line breaks.
Why? I don't know. I just hadn't noticed until now. If you're someone who puts a lot of history or description into your characters, this is kind of awful. Kind of really awful. Everything else about it works great, but line breaks just… don't.
I'll look into it and see if something can't be done but I make no promises…
06/17/2022 Edit:
I attempted to fix the "attempt to index field `?' (a nil value)" errors for lines 637 and 793. There were unnecessary line breaks. I dunno. Weird.
(Spoiler: It didn't work.)