Whichever record was last updated is the one that will "win".
To prevent this from being able to be updated you can set up field blocks under the admin section for the particular sources you wish to not allow updates to occur from.
Once a value is set, it will not be updated by any of the checked options here.
Thanks for your reply Geoff!
As of now, we only wish to exclude the name from being updated in Salesforce after a sync occurs.
Which of these values would you suggest be selected to prevent that change from happening?