Edit: I think I can't move pointer on TV using controller any more because it's input is being captured by that screen at that point. May be assign a random name and give option to change the name.
Edit: Used Shields app to move pointer like actual mouse and was able to enter name and play the games.
Feedback: it might help to show who is controlling the screen at the moment when browsing games. I was connected with phone and my kid was on controller and initially I was mashing keys on controller to actually start the games (pressing A to start). Realized later than since I am the leader may be I should press A on the phone screen.