register on (something)
1. To enter one's name on a website or software application. You'll need to register on our mobile app before you can start using our service. My wife registered on the website two years ago, but wasn't able to remember her password.
2. To enter someone's, something's, or one's own name and details on an official list or record. In this usage, a noun or pronoun is used between "register" and "on." I suggest registering each of your family members on the State Department's website before you travel. She registered the business on a database of recruiters to help find new employees.
register on something
[for an effect] to show on something, such as someone's face. Recognition registered on her face when she saw the photograph of Walter. The total of the votes registered on the large Scoreboard at the front of the hall.