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The possessive form of the proper noun Eugenia is Eugenia's.
example: I met Eugenia's brother at the party.
Eugenia Tuttle's birth name is Eugenia Ash.
Eugenia Paul's birth name is Eugenia Popoffon.
Eugenia Zukerman's birth name is Eugenia Rich.
Eugenia Cauduro's birth name is Eugenia Cauduro Rodrguez.