I assume that "Name only" option results in the push notification only sending "Signal message from Bob", and the "No Name or Content" one only sending "You have a new Signal message" - instead of the whole "Signal message from Bob: Let's rob the bank tomorrow!"
If I could have it work the way I'd prefer, Signal would let me set those Notification Content on a per contact and per chat basis - so I could set my bank robbing crew and group chats to "No Name or Content" while leaving mom and the family group chat on "Name, content, and Actions".
(But realistically, if I _did_ have a bank robbing crew they'd all be on my burner phone, not the phone I do family group chat with.)