To merge contacts in Salesforce Lightning Experience, open one of the duplicates, click View Duplicates in the Potential Duplicates panel, select up to three contacts, choose the principal record and the field values to keep, and click Merge. The other contacts are deleted and their related records move to the principal contact; the merge can’t be undone.
I merged real duplicate contacts in a Salesforce Developer Edition org and captured every step, including the case where Salesforce shows “no potential duplicates” even though two contacts have the same name. I also tested merging contacts from two different accounts.