Why doesn’t he tell his friends about me?

There’s a guy I’ve been talking to on Facetime for a couple of weeks now but I have been seeing some red flags which I’d love to know your thoughts on. He told me he’s a very private person and he has mentioned that he only gets along with a specific kind of person. This is fine I guess but I’m worried it means he is quite secretive possibly.
So he does this thing where he’ll be finishing off his video game with his friends when I Facetime him, then when he tells them he’s gonna go, he makes up an excuse like telling them he’s gonna go get dinner or go to sleep - instead of telling them about me. He told me it’s only because he knows they’ll bombard him with questions about it and he said he’s the type to not tell unless he’s asked. I understand that but my ex did a similar thing and he ended up ignoring me at school which I hated and he didn’t want to change even though he knew how it made me feel. I don’t need to be shown off every day but I want to at least feel like they’re somewhat glad to be talking to me.
This type of thing kind of makes me feel unwanted or like he’d be embarrassed of me rather than proud. Im wondering if you’d see this as a red flag or more of a personality trait of his?
Why doesn’t he tell his friends about me?
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