he called me by his ex girlfriend’s name

so basically the title. we have only been talking for a month but not officially dating. i (23f) really like (37m) him and i like that we have good chemistry.

a frequent problem we have, however, is how often we talk about his ex gf. there was some difficulty in the beginning of our relationship with her bashing him and his character (they were broken up but she was upset he moved on), we navigated through it within the first week or so and it was mostly over. i then asked very nicely that we don’t talk about her so much because we are working on being together and i don’t want her to be a focal point in our relationship. well that didn’t happen. at the bar we all frequent, people who heard about the commotion with his ex would then talk to him about the drama. every time this happened, he would get blacked out drunk and not remember much of the night. i was also never around when it happened so i don’t know how exactly things unfolded. i eventually broke it off with him because that was a big red flag to me and because i didn’t want to work on this issue when i have bigger issues going on in my personal life. but unfortunately i still missed him. we spoke for the first time last night since the break up.

i opened up to him about my personal family issues and how i felt about his ex gf. i decided in that moment, maybe it wasn’t fair to break it off because he was still trying to be supportive of me regardless of our status. so after being vulnerable with him and feeling comfortable with the situation, he called me by his ex gf’s name. he quickly apologized and said he had been drinking and accidentally slipped up. but my heart immediately sank. the phone call ended pretty quickly after that. i think he could tell by my tone i was upset so he apologized again over text. i know he wants to work on us and date but that was honestly a big blow to me. is it worth it to navigate through this as well or should i end the relationship?

(sorry if this story is choppy, any further clarification can be added to here or the comments.)

tl;dr: man that i’m talking to accidentally called me by his ex’s name after i was vulnerable with how i felt about her and our dating status.