How can I “unblock” my name under iPhone settings?

If so, you should better secure your iPhone so that no one can access it.

Never leave your iPhone unattended.

Use a passcode.

Change your Password.

Create a strong password for your Apple ID, It is best if your password consists of eight or more characters and include upper and lowercase letters, and at least one number. You can also add extra characters and punctuation marks to make your password even stronger. 

Never provide your password, passcode, security questions, verification codes, recovery key or any other account security details to anyone else. Apple will never ask you for this information.

Then see this Apple article: What to do after you change your Apple ID or password

What to do after you change your Apple ID or password - Apple Support

See also the following Apple articles:

Prevent in-app purchases from the App Store

Prevent in-app purchases from the App Store – Apple Support (UK)

Delete suspicious content from your devices

Delete suspicious content from your devices – Apple Support (UK)

Never jailbroken your iPhone.

Do you have a MDM profile?

If so, contact your compant - IT department.