How to remove suggested contact from Messages search?

Suggestions are based on how you use your iPhone. The more you interact with a contact, the more prominently that person will appear in suggestions. Contacts you rarely or never interact with typically won’t be suggested.

Gecko209 wrote:

Totally get that, but he is my boss and even when I have personal focus filtering his face is still there.

Focus has no effect on your ability to contact another person. It only regulates what notifications you receive. If you message your boss frequently, you're going to see his contact information when you search.