How can I load a playlist from my Mac to my husband's phone since it keeps naming his phone as mine?

My husband does not do technology and I can no longer add music to his old iPod when I plug it in to my computer. So, I bought him AirPods and am now trying to transfer a playlist to his phone. Easier said than done.

When I plug in his phone it says it is MY phone and doesn't pick up his device or its name. When I select 'new' phone, it still wants to call it MY phone. Why won't it recognize that it is a different device? I don't want to mess up the playlists on my devices, but there is nothing offering a clue as to how to make it recognize his phone.

I tried to set up family sharing, but that apparently only works for stuff you've purchased (and I'd really prefer to keep my stuff separate as less tech works better for him). Most of the playlist is stuff copied from CDs which would work just fine, if only I could simply transfer a playlist from MY computer to HIS phone.

Help!