How do I remove a contact from Airdrop?

Every time I click on the share box on Safari, the name of one of my contacts appears at the top. It is a contact who I would never want to share anything with and I am concerned that I could accidentally share things with them as it is so prominent.

Is there a way to chose which contacts display under Airdrop rather than a blanket all or none? The only solution I have found is to delete a useful message thread I had with them! This is surely not the only solution?

This has occurred since installing IOS iPad 13