Change device names on the devices themselves. On iPhones and iPads at Settings > General > About > Name. On Mac computers at Apple menu > System Preferences > Sharing > Computer Name.
Also, sharing an Apple ID is usually not recommended as it results in iCloud data being synced (including deleting from all devices when something is deleted from 1 device) when you may not want it to. You can still share selected things if desired by using Family Sharing. Family Sharing - Apple
But be aware than changing to separate IDs is not easy if you have been sharing for some time.