5 years ago I divorced, we had to children which live with me. However they still bear the family name EDITED. I later got involved with someone else and we had a child who we gave his surname EDITED. A few months back I found out that he had been cheating on me. Our child together is not yet 2. He had been seeing someone else for months and now they are living together. I feel it is important for the youngest child to take my name as now as only the eldest two have the same name.
Child 1 EDIT
Child 2 EDIT
Child 3 EDITED
Mother EDITED!

I feel a name is important and shows recognition to your other family members and a sense of belonging. I therefore want to change Child 3 to EDITED! - Can I, and How do I go about doing this?

This is a legal issue not a parenting issue. So its been moved to this forum. Please pay more attention to posting guidelines. There is a Read First sticky at the top of the Parenting forum that directs legal question here.

A birth certificate is a legal document and cannot be changed, except by court order. You would also have to get the father's permission to do so.

5 years ago I divorced, we had to children which live with me. However they still bear the family name EDITED. I later got involved with someone else and we had a child who we gave his surname EDITED. A few months back I found out that he had been cheating on me. Our child together is not yet 2. He had been seeing someone else for months and now they are living together. I feel it is important for the youngest child to take my name as now as only the eldest two have the same name.
Child 1 EDIT
Child 2 EDIT
Child 3 EDITED
Mother EDITED!

I feel a name is important and shows recognition to your other family members and a sense of belonging. I therefore want to change Child 3 to EDITED! - Can I, and How do I go about doing this?

It is never a good idea to post real names on a worldwide website. Especially that of a child. Your post has been edited to delete the surnames of the children.