Texts from husband show as from myself I receive a notification indicating I have a new text from my husband - showing his name/contact.  After clicking on the notifcation from him and reading the text, my Messages show the text came from me, my name/contact, but have the content of his text message.  We are on the same family share Apple ID.  Only my number is in Settings/Messages/Send &amp; Receive and checked.  Not enjoying what appear to be text messages from myself.  lol.
There are three ways a name shows up on iOS. 


Apple ID - if the sending phone is signed in with an AppleID that has your name - you will see that name and can’t change it on the receiving end. Sign out of iMessage and FaceTime on the sending device. Then sign in again with an account that isn’t in your name. 
Your address book matches the email or phone number with iMessage (if blue) or sms (if green). You can clean your address book and fix the name. 
All the other content. This one is harder to fix. 


The last bucket uses spotlight index to search content on your phone and try to match that an email or message naming “Joe” also has joes email or phone number. Enough hits between the same name and number and iOS “suggests” who the message is from. 

If you can upload a screen image of your device we might be able to help narrow down or show you how to tap on the name and get to the matching contact and clean this up.