Looking for name of a double ended connector
This question would probably receive a better answer on Woodworking SE.

According to Wikipedia, as well as Canadian Woodworking, this is called a Dovetail key, Dutchman joint, or Butterfly joint. Another common name for it is a Bowtie joint/key. Below is the picture shown on Wikipedia:



Dovetail keys are used to hold together two boards or one board that has begun to split (to prevent further splitting). In this Youtube video, a woodworker further elaborates on its uses and also demonstrates how to make one.