The Church will register at least 1, but no more than 2 names. If not a single Godparent, then 2 Godparents ( a God Father and a God Mother); or in the case of one party being not Catholic, that of a God Parent and a Witness.
A family might choose to have an additional person called a God Father", but it would be totally ‘unofficial’ and weither or not they would be allowed to participate in the offical functions of the God Parent would be entirely up to the Priest or Deacon officiating.
Discuss this with the Priest or Deacon who will be doing the Baptism and get their input. If they say ‘No’ thats that.
In any case only 2 persons will be registered with the Church and will officially have a role in the Baptism.