As an example, I believe to recall the first time I felt this way as a child, perhaps age 4 or 5. There was some sort of a meeting and somehow a kid felt prompted to go up to the whiteboard and start explaining everyone the Bionicle alphabet (https://bionicle.fandom.com/wiki/Matoran_Alphabet) with unreasonable enthusiasm. I was into Bionicles myself, but remember thinking to myself, "Don't you know how you look like? Don't you know that nobody cares? Have you no sense of how others perceive you? If I hadn't seen how this looks like, would I have done something like this eventually?". I don't know how others brush these impressions away with a "Good for him".
Anyway, to answer your question: I'm not sure there's any personality traits I would call "embarrassing". There are some I would call harmful, sure, and there are some that are associated with being socially inept or less cool, but I don't think there's a category of personality traits that are just embarrassing.
To your specific example: Being enthusiastic about things isn't embarrassing; it invites others to share that enthusiasm, either because of a shared interest or simply because watching someone be enthusiastic about something is enjoyable.