I understand that the father of Mary in the Bible is Joachim but in the Quran the father of Maryam is Imran and she is also called by her nation as the sister of Harun. How does one reconcile these differences?
There is no contradiction at all. Mary (Mariam in Arabic) is daughter of Imran as Quran mentioned (And Mariam daughter of Imran who guarded her chastity) (Sura 66, Verse 12). She is also known withing Bani Israel as sister of Haroon (O sister of Haroon , you father was never a bad person nor you mother was a bad woman) (Sura Mariam, Verse 16).
Joachim can be the name of Imran in another language.
Wassalam.