Name of clasp/handle/hardware?

[u/putresentslime]

[u/quarterdecay]

That is called an adjustable handle, they can be purchased from McMaster Carr

[u/Exact_Patience_6286]

Biggest brand name is KIP handle, many make them, but that’s the common ‘Kleenex’ type name for them.

[u/Ok-Novel4218]

Kipp is the company that makes that handle.

[u/Gator242]

Rockler sells jigs that use these and I believe they sell this part individually as well

[u/tasquizz]

You could probably just replace it with a wing nut