Two people trying to add the same surname simultaneously is already handled because add_surname.cgi first checks if an entry already exists for the surname in question.

This makes two people adding the same surname less likely, but not impossible. Imagine your code is like this:

1. Check if surname exists
2. Add surname

and you have two clients, Alice and Bob, both adding the same surname. If things happen to be ordered like this:

Alice: Check if surname exists (it doesn't)
  Bob: Check if surname exists (it doesn't)
Alice: Add surname
  Bob: Add surname

you'll have the same problem. One solution is to enforce only a single surname in the database, with UNIQUE constraints on columns.