If you logged in via the NYC.ID log in (on the Hats & Ladders log in page), you can add your name to your profile by doing the following:
1)Log out of Hats & Ladders
2) go to: https://www1.nyc.gov/account/user/profile.htm and log in
3) add your profile name
4) go back to Hats & Ladders and log in again
If you logged in via Google, you can add/change your name by following these instructions:
To change your name in Google, you click on the icon in the top right corner (it is either a letter or a photo) and then follow the instructions for managing your google account. Then you can change your name in Google and it will change your name in Hats & Ladders too.