Currently there is no option from the Location record to add a custom field and use as an Identifier. This is an alternate solution so you may use the Location Record as a filter to your custom field.
1. Navigate to Setup > Company > Locations.
2. Edit Any Location.
3. From the Address tab, find a field which you are not using. (Example: Attention)
4. On the Attention field, enter a value: Custom1
5. Click Save.
6. Modify your Custom Entity Field which is a List/Record: Location type.
7. On the Sourcing & Filtering Tab add the Filter Using: Attention | Compare Type: Equal | Compare Value to: Custom1
8. Click Save.
Now the values on your custom field when viewed should only contain Locations which has a value of Custom1 on the Attention field.