There are many variations on monogamy and non-monogamy and each relationship is different. The most important parts are being true to your yourself, communication and trust.
Monogamy and non-monogamy are independent of sexual orientation and gender identity.
Monogamy is a form of relationship in which an individual has only one partner. Some people consider this to be one partner for life, others consider any number of partners monogamy as long as one relationship finishes before the next begins ("Serial monogamy").
Like so many terms, monogamy has a spectrum of definitions and definitions.