The name of Bugsworth derives from one Ralph Bugge, of Nottingham, an erstwhile woollen trader, who diversified into lead mining in Derbyshire, becoming Bailiff of the Forest in the Peak in 1250. His enclosure, land bounded by the Wye, Etherow, Goyt and Derwent rivers, became known as Buggesworth; the 'ge' was slowly dropped during the 17th century, becoming 'standardised' in the 19th century as Bugsworth.
Attempts to change the name, prompted by the villagers' rebellion against a town named after 'bugs', or pestilence, began in 1874. The names 'Lymedale', or 'Limedale' were proposed; Buxworth was suggested as early as 1900-01, but it wasn't until 1929/30 that agreement locally was reached, and 1935 before the name was changed officially by the Derbyshire County Council to Buxworth.
Due to either a late-1990s embracing of all things 'organic', bugs and all, or the perverseness of human nature, an attempt was made to rename the village to Bugsworth for the Millennium, which went so far as a village referendum taking place. The change has apparently been rejected, at least for now...
A series of articles by Keith Holford about the change of name have been published in the Derbyshire Family History Society Journal, Branch News, Issue 91, Dec 1999, pp30-31; Issue 92, Mar 2000, pp28-30; Issue 93, June 2000, pp26-27; Issue 96, Mar 2001, pp23-25, to which I am indebted for the factual information in the above brief summary.
Accoring to Wikipedia, locals refer to the place as "Buggy".