The TBL file extension is traditionally used for tables, usually textual semi-database file types.
These files contains mostly text data formatted in some sort of table. They are used in Persona 3, 4, and 5; however, the TBL format in Persona 5 may differ from the format of the same name in Persona 3 and Persona 4.
The PersonaEditor by Meloman19 allows one to view TBL files from Persona 3 and Persona 4.
You can edit Persona 5's NAME.TBL file with the Persona5NameTableEditor by ShrineFox.