1) Any pest 2) Bother 3) Many a little brother 4) Nudnik 5) Nuisance 6) Persona non grata 7) Pest 8) Someone given to teasing 9) Tease 10) Teaser 11) Unwelcome person 12) Vexer Found on https://www.crosswordclues.com/clue/annoyer
annoyer 1. Someone given to teasing; as, by mocking or stirring curiosity. 2. A reference to anyone who disturbs or irritates; especially, by repeated acts of harassment or quick brief attacks. 3. A person who wears on the nerves of others with persistent-petty unpleasantness. Found on http://www.wordinfo.info/words/index/info/view_unit/4045/