A person who gives compliments; someone who praises or flatters.
From 'compliment' + '-er' (agent suffix forming nouns for people who do something). This straightforward agent noun follows productive English patterns for naming people by their actions.
Agent nouns with '-er' are one of English's most flexible word-formation strategies—we can apply it to almost any verb to name someone who does that action, which is why 'complimenter' is immediately understandable even though it's uncommon.
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