More often than not, we are unable to find a primary source for a given first name at birth - or during life (signature on a document, for example). We may have a town record where it is spelled several different ways, depending on the spelling ability or ear of the clerk who entered it, on birth, marriage,or other events. Here's the late 1700s example that triggered this question: Her birth was entered in the town record as Hephzebath. Her marriage was entered as Hephzebeth and Hephzabeth. A 1900 genealogy uses Hepzibah for birth and Hepsibeth for marriage. Her profile is for Hepzibah. Her name on her gravestone, and also on her gravestone, is Hepzibeth. She also has a granddaughter whose gravestone is Hepzibeth P (which is likely for her grandmother's LNAB Phelps.)
I am inclined to correct her profile to read Hepzibeth, and mention the alternatives as set forth in the town records. Inviting opinions for or against, and other suggestions.