Which one is correct?
Request you to please arrange to include Richa and mine name in IFRS group.
Request you to please arrange to include Richa and my name in IFRS group.
You could also say "...Richa's name and mine.."
I agree -- it's cleaner. Otherwise, Risha needs an apostrophe, and names should be plural. Risha's and my names.
I think it sounds quite awkward and advocate for euncu's suggestion.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.