Hill & Knowlton Inc., the prestigious New York and Washington public-relations firm, has filed suit in U.S. District Court here against socialite hotelman John B. Coleman. The suit claims Coleman owes the firm $103,148.62 in consultantion fees and out-of-pocket expenses.

The case is one of half a dozen suits filed against Coleman since he bought and refurbished the The Fairfax Hotel here at 2100 Massachusetts Ave., N.W., in 1978.

Coleman is a man who keeps a lot of lawyers busy.

In Chicago, where he owned two hotels before buying The Fairfax here, he changed lawyers so often that his legal peregrinations were the subject of a story last September in The American Lawyer.

Coleman, owner of The Tremont and The Whitehall in Chicago, has -- according to the magazine -- "within the last two years, dropped Winston & Strawn, moved to Schiff Hardin & Waite, and canned the firm for Reuben & Proctor."

Coleman thus far has been represented in Washington by at least three law firms.

Arent, Fox, Kintner, Plotkin & Kahn, which claims it represented him from the spring of 1977 through May, 1979, has filed suit in the D.C. Supior Court charging that Coleman owes the firm $29,215.77 "for legal services perfomed and expenditures incurred."

Coleman is represented in that case by Barnett, Algia & Carey.

In two other suits against him, Coleman is represented by David Povich of Williams & Connolly.

Povich was the lawyer when Needham Harper & Steers Advertising Inc. sued Coleman last year, claiming he owed them $25,153.85 plus attorneys' fees, under a contract with him and The Fairfax.

That suit was settled for an undisclosed amount and dismissed last month.

Povich also represents Coleman in a still-pending suit Coleman brought against the Gore family, from whom he brought The Fairfax. They They counter sued. Each side is claiming it is still owed money in the deal. t

It isn't clear who is representing Coleman in a suit filed last month by two Arlington painting contractors, the Hudson-Shatz Painting Co. Inc. of 110 Uhle St., and the North American Painting Co. of 4949 N. 33rd Road.11Road.

In a case filed in the Superior Court, the painters claim Coleman owes them some $70,00 for work done on The Fairfax between May 1, 1978 and January 1979.

Coleman has not yet been served papers in that suit, according to the plaintiff's lawyer, Allen A. Sperling.

In another suit, the advertising firm of Goldberg/Marchesano & Associates Inc. Claims Coleman owes the firm $7,880.07 for advertising services during the latter half of 1978. A default judgement was entered for the plaintiff on May 14, 1979, and has since been paid, according to attorney Barry Taff.

Coleman said yester he is "not discussing" any of the lawsuits or his lawyers. "Whatever you want to write, you write," he said.