The following is needed for a series to be a harem in an anime, manga, light novel, or web novel series: At least 3 members of the opposite sex being interested in the lead character (be it love or lust) are needed though the more niche same-sex harems and mixed-sex marriage do exist. Now, whether or not those 3 members need to be living in the same house as the lead is debatable.
Polygamy is having multiple spouses. Having 2 spouses is bigamy. More specifically, having at least 2 wives is polygyny and at least 2 husbands is polyandry! Similarly, polyamory is the practice of being in an intimate relationship with at least 2 partners but there is a consent among the partners to do so. Polyamory is a common practice among the harems where they are not married! However, it can be argued that sometimes a harem has the guy married to the girls from a practical but not legal standpoint!