The correct answer is A. The first blank should be filled in with a semicolon, while the second blank should have a semicolon followed by the word and.
In a list, the items are usually separated by commas. BUT, when the items you are including in the list already contain commas, you should use a semicolon. As a result, "Welsh, Bob" and "Parker, Mandy" should be separated by a semicolon.
Moroever, in a list of items, the last item is usually preceded by a COMMA and the word "AND". But, as I said before, as the items already contain a comma, you should use a semicolon. So "Ross, Wendell" should be preceded by a semicolon and "and".
The sentence would then be "On my list I have three names: Welsh, Bob; Parker, Mandy; and Ross, Wendell."