Learn English – word for a name based on something someone does

How about moniker for the noun?

And I'd be inclined to invent monikerize for the verb.

(I also like appelation, but I don't have the right to up-vote it yet.)

Aptronym is the word for a name aptly suited to its owner. ("Allegedly coined by the American newspaper columnist Franklin P. Adams" 1881-1960. Also see Encyclopedia Britannica.)

(Another word meaning the same thing is "euonym".)

Inaptronym is an ironic form of an aptronym, and examples are given at the link.

Given the linkage in at least one of the references to the word "malapropism", I suggest the neologism malaptronym.

Another possibility (also coined) is misaptronym.

To be more precise, though, the prefix mal- generally means "bad" or "badly" and the prefix mis generally means "wrong" (or "astray"). The prefix anti means "opposite". So a name that means the opposite of what a person does might be antiaptronym. (Contra-aptronym too, maybe, but it's a little hard to say.)