The trainer names may have been different at each of the gyms, but given the identical and oddly specific behavior at each gym, there's a decent chance this is one person using multiple accounts. It can't hurt to report, and be as thorough with the details as you can.
I'm curious, though : you said that 3 Chanseys appeared in each gym, some of which were 20 miles away. How were you able to observe this?