Unlike Chess, there is no established convention other than what was on the box.
Some players who have been around awhile have submitted some names to the Twixt wiki found here:
http://twixt.wikifoundry.com/page/Naming+Board+Elements+and+Peg+StructuresI heartily recommend that anyone interested in the game to review the information available from the pages available at this site. Alan and KD and others have provided much valuable analysis here and I have added my own small contribution.