If she's left alone in Demon World even for five minutes and some punk comes up to her, she will probably try to hold her own until she does have to resort to name dropping. I think by that point, Botan would want to show her own prowess but would also be happy to say she's with Yoko Kurama. It might have more impact if she mentions it than if the scent is detected, but it could be a secondary thing that happens after the demon knows.

I'm certain some girls would want to suddenly cozy up to Botan if they think they can get closer to Shuichi and find out more about him. I swear if one of the girls shows up with her hair dyed, Botan is gonna be unable to hold back to laughter. Even if it happened on say, Halloween, she'd be too amused not to outright laugh in the poor poser's face. Kids these days. But guy talk won't be something Kurama indulges in, or at least I don't see him being able to do so with too much detail. He's a nice boy, high above any pervy gossip. Plus he knows how fast gossip spreads around school. Personal details would be foolish to leak.

A bounty hunter would be an interesting thing. I suppose with him appearing at the DT, people could be more interested in taking him on again. But it would be interesting if Shiori was involved in an attempt to get to Kurama, so he'd then have to tell her about himself? And then soon Botan would be picked as another target? Cue all the bloodshed. And then Botan gets to have 'you saved me' sex with Kurama. <3