I've had both happen. We live in a large city but both attend the games of the professional soccer team here. The first time I saw him we locked eyes for a second and I waved at him, but put my head down rather quickly, so I didn't really see his response. I saw that he was with his partner. I gather from what he said at our next session that he likely ignored me. He said he didn't want to explain to whoever he is with who I am.

The next time, we were both alone. He saw me and waved and smiled to get my attention. I smiled back and said hello but kept walking. I didn't want it to be awkward to stop and have a chat with him. Maybe it wouldn't have been.

I've seen him a time or two where he didn't see me and I just kept walking.

I'm not embarrassed about being in therapy and I wouldn't care if he said hi to me if I was with someone. I think in general, if you're not alone, they should follow the client's lead. If we were both alone, I'd feel hurt if he didn't acknowledge me though.