Contacts not saving

I have been having trouble saving a new contact... once I got to add the name to the number it will save the name for a moment and then remove it and go back to just the number (visible in something like a text message or phone call) - I noticed my iCloud storage was full and was not sure if it was related to that so I upgraded to more storage but the same issue is still occurring. My guess is that it is related to something in my settings on my phone but I have not been able to find anything online of how to go about fixing it and what I have done on my phone has not corrected the issue. Any insight would be much appreciated!