How important are labels in a poly relationship? For example my partner and I do traditional relationship things together. But when I casually referred to him as my boyfriend he said he didn’t want any labels.
That question is impossible to answer; there’s no “Polyamory Prescriptions of Importance” that tell you how important various things are to every polyamorous person. If they’re important to the people in the relationship, then they’re important. If not, then they’re not.
You need to talk to your partner about this and figure out what he thinks “boyfriend” means vs. what you think it means. If, to you, “boyfriend” means “someone who sleeps over, texts me in the morning, and comes with me to work events,” and he does those things but won’t call himself your boyfriend, that is obviously going to feel confusing and oddly arbitrary to you. But if your partner thinks “boyfriend” means “someone who is committed to a long-term relationship and hopes to move toward higher levels of life entwinement like cohabitation,” he might be balking at that term.
Ask him: why don’t you want labels? What does “boyfriend” mean to you that “partner” doesn’t? Is it really just about the word, or is there a different concern? And think about what “boyfriend” means to you, so you can better communicate that to him. How important is it to you that your partner is willing to use that word? Why? It’s highly unlikely that this is really about what collection of syllables you two use to refer to each other - it’s what that word signifies to both of you that needs to be brought from the realm of implication and assumption into clarity and communication.