Hello there, incognito56.
It sounds like you are trying to merge or unify duplicate contacts on your iOS device. The following link to the online iPhone User Guide provides the steps for how to do this on your iOS device:
Unify contacts - iPhone
When you have contacts from multiple sources, you might have multiple entries for the same person. To keep redundant contacts from appearing in your All Contacts list, contacts from different sources that have the same name are linked and displayed as a single unified contact. When you view a unified contact, the title Unified Info appears.
Link contacts. If two entries for the same person aren’t linked automatically, you can unify them manually. Edit one of the contacts, tap Edit, tap Link Contact, then choose the other contact entry to link to.
Linked contacts aren’t merged. If you change or add information in a unified contact, the changes are copied to each source account where that information already exists.
If you link contacts with different first or last names, the names on the individual cards won’t change, but only one name appears on the unified card. To choose which name appears when you view the unified card, tap Edit, tap the linked card with the name you prefer, then tap Use This Name For Unified Card.
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Cheers.