Redesign your database so that each field contains only one name. That would be the best solution (I'm doubtful that MySQL has anything analogous to PHP's explode(), so you'll have to fetch all the rows, explode, filter, then count: renormalizing the database would be better.)
Still don't know if MySQL has it, but if it can count the number of occurrences of a substring in a string type field: count the commas and add 1.