Changing My Last Name- do I need to do anything for my minor child's records? NYS, not NYC

My partner and I will be changing our last names in the next year to match the last name we gave my child when he was born (it's a combination of our current last names).

Once our names are legally changed, I know there is a long list of items we will need to change and entities to inform. Do we have to do anything in regards to our minor child?

I would imagine we need to tell his pediatrician and school, but do any sort of official legal records regarding the name of his parents need to change?

We're located in New York State, outside of NYC. Thank you!