How do I grant a Local Windows Service read/write privileges to a single table

I am running a new windows service that I just wrote. Both the service and the sql server are running on the same machine. It can’t connect to the sql server. The sql server logs show:

Login succeeded for user ‘WORKGROUP\DESKTOP-P9I8PJP$ ‘. Connection made using Windows authentication. [CLIENT: ]

and

Login failed for user ‘WORKGROUP\DESKTOP-P9I8PJP$ ‘. Reason: Failed to open the explicitly specified database ‘JPBPS’. [CLIENT: ]

I can’t see a user WORKGROUP\DESKTOP-P9I8PJP$ for the server or database. But it still connects…

How do I grant a Local Windows Service read/write privileges to a single table?