仕上がる and 完成する are not much interchangeable in Japanese, though you may cover both with English "to complete". It may be better explained from its transitive counterpart 仕上げる, which means "finalize", or in the A を B に仕上げる formula to mean "put A [work] into B [a final form]". As the "final form" meaning is already incorporated in the verb, the argument ～に is used to describe what it is like.
Thus the intransitive one would mean like:
"Nia is (desirably) shaped into a character that has never existed in 『デート』"
"Nia has (finally) acquired a personality that has never existed in 『デート』"