adoptive parents can change the name at any age -- however agencies and social workers are realizing that adoptees sometimes struggle with identity issues and encourage parents to keep them...at the very least, maybe drop the middle name, make their current first name the new middle name, and a new first name. I donlt know of a judge that has required keeping the name, or asked the child what they wanted. Perhaps a few do, but the main decision seems to lie with the parents.
Any child toddler ago or older I personally would be loathe to change, and of an older child I'd ask them what they thought. Some want a new name, to go with thier new family. Some kids have foreign names, so they might find americanized names easier to go with their new citizenship. But I would make sure it was at least retained as a middle name. I think this went along with a very widespread practice where people hid that children were adopted, closed adoption records, and tried to wipe out any vestige of their previous indentity. Many adult adoptees have grown up to say this was harmful to them.
I've also been involved with infant adoptions...both babies I fostered had their names changed...but in some cases the bmoms are aware of the new name ahead of time. Sometimes not, so I think it's still nice to keep a little bit of the birthmom's intent in their somewhere, even if you have a kid with 4 names.