In The Truth, Gaspode wants to help William de Worde investigate the conspiracy behind the committee to un-elect the Patrician. Vetinari's 16-year-old dog Wuffles was a key witness to an incriminating event. However, Gaspode understands the difficulties associated with revealing himself to be the famous Talking Dog of Ankh Morpork. That would provoke more questions than Gaspode would want to deal with.
So Gaspode hides in a multi-storey livery stable. When William arrives, Gaspode identifies himself with the name "Deep Bone."
In the American Watergate scandal of the 1970s, the Washington Post investigated a criminal conspiracy run by president Richard Nixon's cronies. The Post's reporters' major source was a Nixon insider known only as "Deep Throat," who met the reporters in a multi-storey parking garage to exchange information.
Gaspode's nickname resonates doubly -- the "Bone" part refers to his doggy nature. However, "Deep Throat" and "Deep Bone" would both be, shall we say, appropriate names for Seamstresses' Guild members in the Moving Pictures.