I was thinking about this exact kind of issue yesterday, while watching an interview with Jeremy Corbyn, a British politician who has formed a new party that is, provisionally, called "Your Party". The back-and-forth with the interviewer just highlighted how bad an idea this is, with one of them referring to "your party" and the other one also referring to "your party". In some contexts, it's absolutely fine. In others, it's a complete mockery.

I am inclined to agree, however often any publicity is good publicity, and stumbling over the name a bit makes it perhaps more memorable (and takes time away discussing any of the real issues, which might actually have something for people to disagree with).

Ugh I hadn't heard about that. That seems especially silly given 'People's Party' is so well established as how you convey that.