Hyphenated surname / Changing sons name

I have an 8 year old son who has been requesting that he hyphenates his surname to include my husband’s surname which both my younger son and I also have too. My 8 year old is full time in our care but still sees his biological dad every few weeks. He has grown up knowing my husband as his Dad too as well as his biological dad, from the age of 1.5 years old. My son understands that he has a biological dad and a step dad. He also understands that changing his name may involve having to go to family court (a school friend of his has been through the process and told him how it works, I have avoided explaining this to him at this stage). I have always supported my son emotionally when he brings this up but he has been requesting to have his name changed for more than a year now. I have explained that he has the same name as his biological dads family but it upsets him that he is the only one in our home that has a different name.

Has anyone been in the same situation and had their child’s name hyphenated? If so what is the process? Any advice or positive tips on how to support my son through this will be appreciated.

Thanks in advance.