If you are able to post pictures or messages to a Magnet, you're also able to change the Magnet name.
To change the name of a Magnet, tap the "..." icon in the top right corner of the Magnet, and then tap "Edit Magnet Name". In the view that follows, you can see the current name of the Magnet inside the textfield. Now tap the textfield and enter the new name for this Magnet.
Tip: You can also use emojis inside of Magnet names!
Once you've tapped on "Done", the Magnet name will change for every participant inside of this Magnet.
If you want to hide the name of a Magnet inside the Magnet widget on your homescreen, tap and hold the specific widget, then tap "Edit Widget", then turn of the switch next to "Show Magnet Name".