Synonyms for arrogance include conceitedness, haughtiness, and superiority.

Shakespeare.

Affectation, airs, arrogance, big-headedness,conceitedness, display, ego trip, narcissism,ostentation, pretension, pride, self-admiration,self-love, self-worship, show*, showing off,smugness, vainglory

"Conceited" is not a noun; it is an adjective. It describes a person who has an excessively high opinion of themselves, often to the point of being arrogant or excessively proud. For example, you might say, "She is so conceited that she can't stop talking about herself." The noun form of "conceit" refers to an excessive or exaggerated opinion of one's abilities or attractiveness.

synonyn for vanity is: conceit, conceitedness; self-conceit, self-complacency, self-confidence, self-sufficiency, self-esteem, self-love, self-approbation, self-praise, self-glorification, self-laudation, self-gratulation, self-applause, self-admiration; amour propre; selfishness., airs, affected manner, pretensions, mannerism; egotism; priggism, priggishness; coxcombery, gaudery, vainglory, elation; pride; ostentation; assurance., vox et praeterea nihil; cheval de bataille., coxcomb; Sir Oracle.