Sometimes, you may end up with multiple Contacts that have the same phone number.
You can't delete a Contact, but you can assign your active Conversation to the Contact that has the correct info!
Click on the Contact that you want to use, then click the "Assign current contact to this conversation" button:
In the example below, the Conversation is currently assigned to a Contact named "Smith John 888572," but it should be assigned to "John Smith." The process described above can be used to fix this, so that the Template Personalization feature always displays an accurate name!