I'm not sure how an SD with the same name could have been created. Something may have been done outside of ArcFM to copy it in the table directly. There isn't a unique key on the NAME column, so duplicate names are possible.
To open each SD you can change the name of one of the duplicates using SQL in Oracle. For example:
update MM_STORED_DISPLAYS set NAME = "new_name" where OBJECTID = <object id of one of the duplicate-named rows>
Once the name is changed, start ArcMap and select Customize > Toolbars > ArcFM Stored Items Classic.
Select the Stored Displays dropdown in the ArcFM Stored Items Classic toolbar and scroll to the bottom of the list. The original name and newly-named SD will be in the list. Open each one and decide which one to keep. Delete the SD that is not needed.
Your suggestions helped me.