When using the verb to be do you always use nominative for subject and object?
For example:
FEMINAE DOMINAE VIRORUM SUNT.
Or
FEMINA EST PULCHRA
Esse doesn't take objects, but instead has predicates, and its only job is to link the predicates. The predicates are usually in the nominative, but if they're not, they won't be problematic.
Usually, esse does link two nominatives, like Equus bonus est, "The horse is good", but a genitive can also stand alone in the predicate, like Equus est patris, "The horse is father's".
Esse also is used with the dative to show possession. To ask "What is your name?", you say Quid nomen tibi, and to say "My name is", you say Nomen mihi est, which literally mean "What is the name to/for you" and "The name to/for me is". You can think about it like someone giving you a gift. The gift is for you, and it's also yours.
Outside of possession I think you are correct to say that yes, the predicate will agree with the subject in the nominative case.
Technically, the verb esse does not have an object, but has a "predicate" which can be either a noun or an adjective. But you are right in a sense, the predicate does agree with the subject and is in the nominative case.