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In Ancient Roman mythology there was a water nymph named Anna Perenna. This may have been the source of a female given name, therefore the name of a female ancestor (metronym). Perenne looks like a French form.
Alternatively, there is a Breton surname, Perennes. Accent grave over the last e, to paraphrase W.C.Fields. This derives from an old male personal name, Perenesius, probably the name of some obscure early saint. That would be the name of a male ancestor (patronym).