Deduplicate by name AND surname (or vice versa)?
Welcome to CiviCRM SE. Eileen's answer is definitely the right place to start, but you might want to look at a related question that I asked about the built-in (reserved) de-duplicate rules, as they aren't entirely clear from the documentation. It says "NAME" in the description, but actually uses the fields "First Name" and "Last Name" (You have used different terminology. It took me a while to work out how it worked.

See Reserved de-dupe rules

Update: Remembering odd behaviour with my previous issues, I looked again and have found that the de-dupe rules appear to be cached. So if you create a rule, adjust it and try with the new version, the old version is still used. I missed this before because I was checking the database and the rule is updated properly there. If you go to Administer >> System >> Cleanup Caches and Update Paths and select Cleanup Caches then try the de-dupe rule again it works as expected. If you were experimenting, then I expect this is the problem.

Alternatively if you delete the rule and add the new version it will also work.

A note on the page where you edit de-dupe rules to tell you to clear the cache would be very helpful. Let me know if this solves your problem and I'll report it as a bug/enhancement.