My Hero Academia's Shota Aizawa has a pretty cool hero name: Eraserhead. However, it's not a name he thought up; it's actually a suggestion from his friend Present Mic from when the two of them were in school together. This means Aizawa is stuck going by a hero name that he doesn't necessarily want. In fact, his discontent is such that he sternly warns his students to come up with proper, suitable names for themselves.
However, the name Eraserhead actually fits Aizawa quite nicely. It indicates what his Quirk is, fits his personality and most importantly, is a name his friend helped him with. Aizawa likely couldn't conceive a better name for himself if he tried.
Perhaps the most obvious reason Eraserhead works is that it matches with Aizawa's Quirk, Erasure. The Quirk, as the name implies, lets Aizawa nullify the Quirks of his targets for as long as he can keep his eyes on them. As far as names are concerned, Eraserhead and Erasure go hand in hand.
Following the Quirk-name synergy, it's a little trickier to understand why a guy like Aizawa would stick with a name like Eraserhead. He mentions that he doesn't like the idea of being in the spotlight (which is probably why he's a teacher), so he could have chosen a less flashy name. However, the name fits his comedically stern and reserved personality too. Eraserhead derives its name from an old, avant-garde horror film. Aizawa himself can come off as intimidating to anyone who irritates him, which is how he keeps his students in line. Some of his lessons like the fitness test are even designed to instill fear in his students to help them grow.
It's true that Aizawa had his name picked out by a friend, but that's the biggest reason he needs to keep it. As students, Aizawa and Present Mic (then Hizashi Yamada) had a third friend named Shirakumo, who proposed that the three of them form a Hero Agency together when they became Pros. By working together, they could cover for each other's weaknesses and become unstoppable. Following Shirakumo's passing, that dream faded, but Eraserhead and Present Mic can still uphold the ideals behind it. In this regard, it's good that Aizawa allowed Yamada to think of a name for him when he couldn't come up with one on his own.
Eraserhead may come off as a silly name for such a serious guy, but it's also an ideal one. It fits him on multiple levels, including ones fans may not think about. It's also special because it's something he received from a close friend. While he'll likely never admit it, Aizawa probably cherishes the name Eraserheadand because of all that it means to him.