Save as placed file name

Say I have a file DSC_0377.jpg. I can open a this with Illustrator, make changes, then choose File Save As Save as type Adobe PDF

and it will be saved as DSC_0377.pdf, as desired. However if I

• open an Illustrator Template


• File Place the same JPG


• File Save As Save as type Adobe PDF

it will be saved as Untitled-1.pdf. Does Illustrator have an easy way to save using the name of the placed file? I have many JPGs I need to do this with, so I would prefer to not have to do something like copy and paste the file names.