ALTHOUGH Les Brown and His Band of Renown never made it to the top ranks in the heyday of the big bands, the long-lived group has become something of an American institution over the decades.

In 1947, Brown began his long association with Bob Hope, which continues to this day. A string of hits, started in 1941 with "Joltin' Joe DiMaggio," included standards like "I've Got My Love to Keep Me Warm" and "This Could Be the Start of Something Big" (Steve Allen's theme song).

According to Brown, 71, their now-famous moniker was born here in Washington.

"We were playing the old Hotel Roosevelt, an on-air date," Brown says. "In those days all the hotels loved to sponsor the big bands with radio contracts. There was no money in it for them, but it was terrific advertising. Then it was very cheap to put a band on the national radio, just a microphone and a couple of wires.

"That night, one of the guys, our lead trombone player, was missing. We couldn't go on without him, because he played our theme song solo. So the announcer had to ad lib to fill time while we ran around looking for this guy. Finally, we found him, and the announcer said, '. . . And now, that band of renown, Les Brown!' Our ears pricked right up, and we've used it ever since. It was one of those lucky things. I was a little perturbed with that guy then, but now I thank him. People always remember phrases like that, like 'Swing and sway with Sammy Kaye.' "

Brown, who plays sax and clarinet, got his start when he left Duke University with his dance band, the Blue Devils Orchestra, in 1936. "That's quite a few years in this jazz," says Brown with a laugh. "When I graduated, we went out on the road for about a year and a half. Most of the boys had to go back to school, though--parental pressure and all. Most of them had taken a year off from college for the band. So I went to New York and did some work as a free-lance arranger for publishers and bands, then I started a new band and we've been going ever since."

With lyricist and arranger Bud Green, Brown wrote the standard "Sentimental Journey," which he recorded with a young singer from Cincinnati, Doris Day. The record sold more than 1 million copies.

" Day was singing in Cincinnati on WOW, which then was 500,000 watts--it really covered the country," Brown says. "Bob Crosby heard her there and brought her to New York with his band. I heard she wasn't satisfied with him for some reason, so I went backstage and hired her. I tried to get Bob Hope to hire her as a vocalist for his radio show and he said, 'No, she's not well-known enough.' Well, within a year, she was the hottest thing in the movies, and he really had to pay through the nose to get her."

Although Brown says he's delighted by the new interest in the big band sound, he laments the disappearance of the old swing venues, the ballrooms. "There's maybe 10 left in the country where there used to be 1,000, and they and the hotels were the backbone of the business," he says. "And there's really no new big band stuff being recorded now. Not even the great Count Basie is being asked anymore. The only records the companies want to make are the ones that will sell over a million copies. Big band just can't sell like that anymore."

Brown just finished his annual New Year's Eve performance for CBS-TV, with Susan Anton and Leo Sayer at the Las Vegas Hilton. "Dudley Moore came out and jammed with us for the last few minutes of the show--we did a spur-of-the moment blues in the key of F. He's a terrific jazz pianist," Brown says. "Our segment of the show was over, but when our director saw what was happening onstage, he said, 'Put 'em on!' and they just winged it."

And The Band of Renown still gets around, though usually just for a couple week-long tours each year, like the one that will bring them to the Shoreham Hotel Jan. 26. Brown and Band will entertain at a four-hour dance to benefit the Washington Chapter of the Leukemia Society, and will be inducted into the Shoreham's Entertainment Hall of Fame.