I gave my old iPhone to my husband. How do I get his name to appear when I open settings?

What to do before selling or giving away your iPhone, iPad, or iPod touch [or if you received one that had not been erased] - "Use these steps to remove your personal information from a device, even if you don't have it anymore." --> https://support.apple.com/HT201351

See: What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support

and then

Set up your iPhone, iPad, or iPod touch - Apple Support

.