Haha, struggling with something similar myself. I have a Phantom Thief who needs naming. This is what I've come up with so far:
Go with whatever feels natural for your story instead of following trends. If you cringe when writing it... You should maybe change it. If it feels completely natural, then go for it. I feel there's a wide variety of approaches nowadays, so there's no one "wrong" or "right".
Maybe try to think of how they got the name. Was it something the public/internet/fanbase invented, à la Beyhive for and by the Beyonce fans (Beyonce -> Queen Bey(Bee)) or Cumberbitches (Cumberbatch fans)? That can turn ridiculous, but still be believable!
Or is it a name that comes with the power, like Garo, Miraculous Ladybug, or the Sailor Warriors?
Or did the hero/villain come up with it themselves? Why? Was it a spur of the moment (which might end up sounding silly to everyone else) or was it based on something that happened, or is it connected to the reason they became a hero/villain? Then that could be all the justification you need for the name.
But honestly, as long as the story is good and entertaining enough, people will swallow most things. I mean, come on. Super man. Bat man. Iron man. Spider man. Those names aren't exactly the height of creativity in today's world, but they still work for new audiences, because they like the comics, games and/or the movies. Or when you get behind the names of the Naruto cast: They must have sounded so ridiculous to at least some of the Japanese readers. Naruto is a fish cake for goodness sake. Or Nara Shikamaru, which pretty much is the same as calling someone Paris Eiffeltowerson, or Sweden Meatballson. But it worked for its context, the characters were modeled around specific traits, from the names, over their appearances and personalities, to their skills.
In the end, it's all about the nature of your story. If you still feel insecure, find someone to read through it and get a second opinion from!
Also, definitely this: