Quote from the manual below. Since you've already added the key just skip the part about clicking the + icon and adding a key. Just select the profile, go to Control -> Locks, and click the driver icon. Then change driver profiles and repeat for the other driver's keys.
Linking a Driver Profile to a Key
You can link a driver profile to a key (or keys) to allow Model Y to automatically select the correct driver profile when the linked key is detected as you approach the vehicle and open the driver's door. To link a driver profile to a key, first ensure you are using your desired driver profile. Navigate to Controls > Locks and touch the + icon. You can add an authenticated phone, key card, or key fob by following the onscreen instructions. When finished pairing, touch the driver icon to link the key to the desired driver profile. The name of the driver profile will appear under the key to show that it is linked.