Lino is Greek for thread, and trypane is Greek for borer, so "thread-like borer". McIntosh gives the Greek words in a footnote. The prior 'trypane' name in Opheliidae was Ammotrypane Rathke, 1843 and subsequently McIntosh added Tachytrypane and Ammotrypanella.
McIntosh, William Carmichael. (1875). On a new example of the Opheliidae (Linotrypane apogon) from Shetland. Proceedings of the Royal Society of Edinburgh. 8(89): 386-390. available online athttps://biodiversitylibrary.org/page/48403860