Speaking as somebody who works under my real name, I think that it's much less important now than it was when I got into the industry.
I was encouraged to work under my real name because I started working professionally in Illustration in the 00s, when it was still mostly still print dominated and a lot of the money-making work was in running workshops and the like, and a lot of big promo opportunities were in newspapers and similar. I think it's very telling that most creators my age (like older millennials aged 35+) who are better known by their pseudonym than their real name are PoC or trans. There's definitely an element of privilege in the fact that even being gay I'm safe enough having my real name as my creator name in most places because being gay is comparatively accepted in the UK and I'm a middle class cis white woman. Also my family are pretty well known in my local community, so I don't really need to hide them or anything, so that makes it very easy for me.
If you want to have a persona as your personal brand, I say go for it! The best way to do it is to build a big persona that can overshadow yourself and be somebody people can buy into just as much as a real person. Think of people like Yoko Taro or Toby Fox, who while they do work under their real names, have these very over-the top personas and only appear wearing masks, or Hiromu Arakawa, who works under her real name, but never appears in person, speaking through representatives and only representing herself in her work as a cartoon cow. One of the best examples might be SonicFox, the famous pro gamer who always competes in tournaments in a fursuit.
Honestly, while I do sometimes appear in papers and stuff... I have issues with my appearance. My milk allergy tends to cause skin breakouts from even cross-contamination and I have mild dysmorphia that causes me to obsess over imperfections and hate looking at myself; so while there have been rare times I've appeared in papers and things that I've felt looked okay like this:
There's a reason most of the time the Kate Holden you see is a drawing like this:
So ultimately "Cumbrian Illustrator, Kate Holden" is nearly as much of a persona used by the human called Katherine E F Holden as Darth Mongoose is. It's a curated personal brand that happens to be under a name I'm widely known by.
If you feel more comfortable going by a pseudonym and some kind of creator avatar, I think so long as the general image and persona is consistent, and you give the audience enough information to latch onto (like just things like what movies and music you like, or talking about your hobbies) there's no reason you couldn't be very successful these days with a persona that's absolutely nothing to do with your actual name and face.