Removing hyphen from name.

[Spied]

DD has a name containing hyphen.
Think Emily-Grace ( but not ).
I love both first names but just really want to get rid of the hyphen. DD agrees and prefers just the first part and all her friends and family use just Emily.
Where do I start?

All those with parental responsibility agree to the name change, and one of you (preferably both) signs a change of name deed for her.