I have a table like:
id name children
1 Roberto Michael,Dia
2 Maria John,Alex
3 Mary Alexandre,Dia
That's why you'd want to have two tables here.
parents:
id name
1 Roberto
2 Maria
3 Mary
children:
id parentid name
1 1 Michael
2 1 Dia
3 2 John
4 2 Alex
5 3 Alexandre
6 3 Diana
And now you can query this much more effectively with a join or an exists:
SELECT *
FROM Parents
WHERE EXISTS(
SELECT *
FROM Children
WHERE parentid=Parents.id
AND Children.name='Alex'
)