Only after you've established that they have serious interest should you drop a name or two; private capital folks tend to be very well-connected with peers and likely have a direct line to any others you mention. When name-dropping a firm you've spoken to but hasn't actually expressed interest in moving forward, a casual mention can seem more like intentional misrepresentation.

You'll probably talk to a whole lot of "potential" before you find any actual "investors", so don't feel compelled to share anything until you get enough traction to be confident that things will line up the way you expect.