From Discworld & Terry Pratchett Wiki
Biers is a nickname for the pub, it is unknown whether the owner has a formal name for it. The monobrowed bartender is called Igor, but is not one: just try asking him to sew your head back on (see Thud!).
Biers is a multi-level pun: it has an assonance with the well-known bar "Cheers" ("where everybody knows your name" - Angua points out that Biers is where everybody knows your shape), and a bier is a stand used to hold a coffin prior to burial or cremation. This last is particularly appropriate considering the undead clientele. It may also be a reference to Ambrose Bierce, a 19th century humorist and author of various Gothic / horror novels (his best known work is "The Devil's Dictionary"). Bierce disappeared under mysterious circumstances in his 70's. while following Pancho Villa's army through Mexico and Texas, which may explain why the owner of Biers is never seen. Finally, the word "Biers" also refers to the German word "Bier" which means simply "beer".
And if you consider the original name of the pub in context with the monarchy of Ankh-Morpork...