In the blockchain, it is impossible to delete transaction history or the profile address. But you can exit Surf profile and uninstall the app on all devices.
If you know the seed phrase you can restore access to your profile anytime.
To exit a profile in Surf:
At the top of the home screen, tap the nut icon.
In the Settings, click Safety protection.
Click Delete local data and exit.
Click Backup to save the profile seed phrase.
Confirm your action with your a PIN code, by scanning your fingerprint or using facial recognition.
Read the safety rules for the seed phrase and click Got it.
Enter your seed phrase to make sure it is saved correctly.
Click Log out without backup.