If someone wasn't previously known, only an alias or alter-ego, but you then link those together with a real-life identity, that's very much the definition of "doxxing", at least the original definition, maybe it's different today? Positive or negative doesn't really matter, just like "shooting" or "jumping" in itself isn't positive or negative, it's just a verb.
And if the police actually catches the accused and puts them in jail, is that kidnapping? Most verbs have far more semantics than just the most basic before/after state diff.
If you want an alias that's fine, just don't use it to do crimes.
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No, if I kidnap someone it's kidnapping. If the police based on probable cause receive and execute a warrant for someone's arrest, it's an arrest. This is how the state monopoly on violence works.