Are you together?
It may seem like a strange question, but are you really together if he doesn't call you HIS girlfriend? He might be actively or passively seeking another partner. Even though you are living together, married, and have children, it does not necessarily mean he is fully committed to you.
If a man introduces you to his friends, acquaintances, and relatives as simply "This is Sarah" without any prefix such as "my girlfriend" or "my partner," it could be a sign that he doesn't view you in a romantic or committed relationship. Additionally, if he only refers to you as a "friend," "acquaintance," or "colleague" it could also indicate that he does not see you as his girlfriend.
The truth is, if a man doesn't introduce you as his girlfriend or partner to his family and friends, it could be a sign that he's not fully committed to the relationship.
The reason is always the same - in the eyes of these people, he wants to appear free. He doesn't want to be associated with any obligation or responsibility. He doesn't want to be seen as "taken" or "unavailable." He wants to keep his options open. And if he doesn't consider you his woman, it means he's not serious about you.
It's important to have a conversation with him about where you both stand in the relationship and if it aligns with your goals and values.