Commemorating the birth of a child remains, for many families, an important event. A chance to mark the occasion in a very personal and special way in front of the nearest and dearest family and friends.
Many look for a ceremony which is simple and relaxed but completely bespoke and personal. I would write a ceremony that is tailored to you and your family, you can make your individual promises to the child(ren) for their future.
You can still allocate significant adults to help with the child's upbringing, indeed the term Godparent is one which is nationally recognised and since it holds no legal obligation it is a term which can still be used in your naming ceremony.
What better way of officially welcoming step-children or adopted children into their new family than with a celebration ceremony all about them!
In just the same way as a naming ceremony, you can use the event to share your promises to the child(ren) and your hopes and dreams for their future. You can also allocate special adults to take on the role of significant adults / godparents.
Older children may well like to participate fully in the ceremony by reading a poem, or participating in a symbolic action such as mixing sand. The mixed sand can signify the joining of the family, much like sand cannot be separated once mixed, neither can the bond of a family.