Oh, this is an interesting thread
I went through a "rebranding" fairly recently, about a year ago or so. Truth to be told, not much thought went behind the choice of my nickname: Llyrel was a name I made up for a RPG character I never got to play. It seemed to be available on most social media platforms I used, so I went with that. Had to use "llyrel_draws" as a variant in some places (like Twitter and Instagram), but other than that, I try to keep my nickname consistent everywhere I go, so that my stuff is easier to find.
I... don't really watermark my stuff. As my professor in Uni pointed out once, watermarks don't really do much to prevent theft: anyone who knows their way around Photoshop or any other digital art program could easily edit your pic to remove the signature, unless you make it so big that it covers a good chunk of your artwork (like it happens on sites like iStock and such). And honestly, even that wouldn't stop people from tracing your artwork. What I do instead is only upload smaller versions of my artworks: pictures are never larger than 800-900 px in height or width. My originals are usually much bigger than that, and all in print quality. If someone were to steal my art, I could easily demonstrate that I have the bigger, print format originals. I should definitely consider adding at least a little signature for people who want to find more of my stuff, though 
As for my social media presence, I post my art mostly on Pillowfort and Instagram, these days, plus a few more places.
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Pillowfort is more of a personal blog type of thingy: you get my artworks and artwork WIPs, but also photography, resin stuff and other artsy things that aren't necessarily drawings. Given the more private nature of the site, it makes more sense for me to use a more relaxed approach on there. I also promote my comic on PF, though honestly what's been more successful on there are my watercolor pieces... even got to sell a few prints on Redbubble thanks to the Pillowfort people!
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Instagram is what I use for my finished or almost finished pieces. I try to join memes/challenges/events when I see one that I like and I use it to post teasers from my comic. Not sure how many people from Instagram actually click on my comic, but the posts themselves seem to do pretty well XD
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Deviantart is where I pretty much only post fanart nowadays. I've got a couple of witchy illustrations featuring characters from my comic, but I market them as "tarot card illustrations" rather than "OC drawings", since I never really had any success with my OCs on there XD the place is kind of a wasteland nowadays and only a few people still seem to care, but eh, I've been on the site for 13 years now and I'd feel bad deleting my account.
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TikTok is what I use to post WIP and speedpainting videos. I'm not an actor and English is not my first language, plus I refuse to show my face on there, so speedpaintings are all you're going to see XD I don't update often, so I don't have -huge- numbers, but so far I'm happy with the number of views and likes I have on there.
I also have a Carrd with links to all of my social media, my Redbubble shop, Patreon and comic. I used to have a Linktree before, but I think Carrd looks nicer and I LOVE how it lets you have different sections for each category: I can have a whole "page" dedicated to my comic with a proprer summary and links to all sites where it's being hosted, instead of just a list of links, and I think it's amazing.
So far, the biggest suggestion I can give beginners is:
Take your time to study each platform you decide to join, see what's popular and how to make it work for you. Try to figure out which is the best time to post, what are the popular tags people use, the kind of content people want to see on that particular platforms. Some platforms work better for fanart (Deviantart, Tumblr), others mostly care about consistency (Instagram), entertainment or tips and tricks (TikTok). Some platforms are better suited to talk about personal content (Pillowfort, Tumblr to a certain degree, your own personal Facebook page) while others are better used for professional stuff only (Twitter, your Facebook artist page). Also... picking a theme and sticking with it might be a good idea. Don't use your Instagram art page to post food pictures, don't suddenly turn your comic promotion Twitter into a place to rant about the season finale of your favorite series (it's okay if you've been using a more personal approach since the beginning, but if you go from art promo only to completely unrelated stuff... it might be a little trickier). People want to know what to expect from your platform, and if you're inconsistent with the type of stuff you post, attracting a following will be more difficult.
...Phew, that was long! Hope it helps in some way 