It does not look as if this is confusion between two local restaurants. Uncle Julio's Restaurant group operates three restaurant brands:

https://unclejuliosrestaurantgroup.com/

...with locations in a dozen states:

https://order.unclejulios.com/locations

Perhaps all brands/locations use the same merchant account. I don't see that this is anything that American Express can "fix", in the sense that they cannot force each location to use a merchant account with a name that matches the restaurant. Is there a store number, or similar, in the transaction description?