If you do not wish so that your username would come up in the search for other users, you can opt out from "Discoverable by username" in the Privacy settings.
For that, head to the 'Payments' section, tap on your username and select the "shield" icon in the top right corner. This will open the Privacy settings.
If you choose to turn off 'Discoverable by username' then other Revolut users will not be able to find you in search, but they will still be able to find you if they tap on your username link.
If you wish to not be identified as a Revolut user at all (either by mobile number or by username), you can switch off 'Payments with friends' in the Advanced Privacy Settings.