Do all your devices have the current software. My iPhone is my main device and keep it backed up and my iPod and iPad update to the same info on iphone. The iCloud shows info from phone. It is good to keep icloud backed up
incase you need to do a sudden reset of phone and lose all your information. Have you tried deleting contact and reinputting contact then backing up. Is your information correct in imessage settings. In settings; your name; iCloud
now has a message button; have you turned it green? That was added in last update and not everyone knows it is there. Have you updated your devices to the current iOS version.