322 And bow them to your gracious leave and pardon.
323 KING CLAUDIUS.
324 Have you your father's leave? What says Polonius?
325 LORD POLONIUS.
326 He hath, my lord, wrung from me my slow leave
327 By laboursome petition, and at last
328 Upon his will I seal'd my hard consent:

The source and name of Polonius have received quite a bit of attention. To quote Wikipedia:

The literary origins of the character may be traced to the King's counselor found in the Belleforest and William Painter versions of the Hamlet legend. However, at least since the 19th century scholars have also sought to understand the character in terms of Elizabethan court politics.

Polonius was first proposed as a parody of Queen Elizabeth's leading counsellor, Lord Treasurer, and Principal Secretary William Cecil, Lord Burghley in 1869. Israel Gollancz also suggested that Polonius might have been a satire on Burghley. The theory was often finessed with supplementary arguments, but also disputed. Arden Hamlet editor Harold Jenkins, for example, criticised the idea of any direct personal satire of Burghley as "unlikely" and "uncharacteristic of Shakespeare".

Gollancz proposed that the source for the character's name and sententious platitudes was De optimo senatore, a book on statesmanship by the Polish courtier Wawrzyniec Grzymała Goślicki, which was widely read after it was translated into English and published in 1598 under the title The Counsellor. "Polonius" is Latin for "Polish" or "a/the Polish man." The English translation of the book refers to its author as a statesman of the "polonian empyre".

In the first quarto of Hamlet, Polonius is named "Corambis". It has been suggested that this derives from "crambe" or "crambo", derived from a Latin phrase meaning "reheated cabbage", implying "a boring old man" who spouts trite rehashed ideas. Whether this was the original name of the character or not is debated. Various suggestions have been made to explain this. G. R. Hibbard argues that the name was originally Polonius, but was changed because Q1 derives from a version of the play to be performed in Oxford and Cambridge, and the original name was too close to that of Robert Polenius, founder of Oxford University. Since Polonius is a parody of a pompous pseudo-intellectual, the name might have been interpreted as a deliberate insult. The title page of Q1 specifically states that the play was recently performed in London, Oxford and Cambridge.