Link sheet name to part name

I link the part file name to the title block as a sheet or drawing number

Go to the drawing and edit the sheet format and type in $PRPSHEET:"PartNumber" then go to your part custom properties and link the custom property PartNumber to what I show below...

Cameron,

You can't have the sheet name (which shows up on the tab at bottom) linked to part properties.  However, if the reason you're wanting it linked is for a note in the title block, you can replace the sheet name note in the title block with a note that's linked to a part property (such as the part name).