How do I change the name on my new Apple watch? It has my husband's name on it.

See: Change the name of your Apple Watch - Apple Support

Check the name in the following places;

On the phone in Settings/general/about

And in the watch app on the phone in General/about

And on the phone contacts app tap on name to change and tap on edit in the top right corner.

Open the Watch app on the iPhone, then go to General > About. Make sure your name is listed here

Also in General, tap on Apple ID to ensure your Apple ID is signed in.