Tennis With King Gustav, Golf With Crosby : THE SALAD DAYS<i> by Douglas Fairbanks Jr. (Doubleday: $19.95; 412 pp.) </i>

The next sound you hear will be Douglas Fairbanks Jr. dropping a name. And another. And another. And another. And another. Give up yet?

Young Doug isn’t even breathing hard. If who you knew was a criteria for literary excellence, these agreeable memoirs would be right up there with Caesar’s commentaries. When Fairbanks confesses to the habit of “throwing names about like grains of rice at a wedding,” he is not kidding.

Fairbanks came by the name-dropping habit honestly. His father was Douglas Fairbanks Sr., the robust idol of millions; his stepmother, Mary Pickford, America’s favorite sweetheart. Together, “they enjoyed a status in the world’s imagination that is totally inconceivable and incomparable by today’s standards,” and being linked to them was both Fairbanks Jr.’s fortune and his undoing. It opened doors to wealth, prestige and celebrity (not to mention a career as an actor) that would otherwise have been way beyond his reach, but it also burdened him almost fatally with an impossible legacy to live up to. “I had spent most of my life,” he relates at one point, “hoping to be worthy of my name and to win Dad’s approbation.”

Along the way, Fairbanks met an almost inconceivable number of famous people. He says hi to an old gent in Holland, and it turns out to be Kaiser Wilhelm II. He notices a lost soul at a British party, and it’s Lawrence of Arabia. He shares a Berlitz course in Spanish with “a polite, rather toothy young fellow,” and it’s future President John F. Kennedy. He takes a trip to Brazil and becomes perhaps the first person ever to dance the samba in public. He buys marijuana for Tallulah Bankhead, serves as a go-between for Greta Garbo and John Gilbert, plays tennis with Maurice Chevalier and King Gustav V of Sweden (not at the same time), golfs with Bing Crosby and sees the 1924 Olympic spirit that “Chariots of Fire” is based on. And he becomes such a good friend to the British Royal Family that he first meets Queen Elizabeth II as a tow-headed toddler in a London garden.

It is in the realm of show business acquaintances, where Fairbanks’ chumminess really knows no bounds. Not only did he go to grade school with Jean Harlow, Carole Lombard and Joel McCrea, but through his father, he formed close relationships with Charlie Chaplin and John Barrymore, despite the latter’s “deliberate ‘image-spoiling’ habit of deeply and leisurely picking his classical nose.” He knew Laurence Olivier when everyone felt it was his wife, Jill Esmond (remember her?), who had the real acting talent in the family, and he met the future Merle Oberon when she was a pretty young “dance hostess” at a London restaurant. He got a large USC guard named Marion Morrison his first two picture jobs, and John Wayne was born. He commented positively on a screen test by a personable young Australian, and Errol Flynn was launched on a career. He tried hard to get a young English actress to give up the stage for the screen, and eventually Greer Garson took his advice. Et cetera.

Fairbanks tells all these tales in a curiously genteel style that is appealing though it occasionally makes the book read as though it was written by Manners the Butler. The first cowboys he meets, for instance, are described as “illiterate, knavish roughnecks of limited ability.” And Fairbanks does have a nice eye for anecdotes, like the time he and some pilot friends decide to buzz Noel Coward’s country house early one Sunday morning. The unflappable Noel responded by having all the pillows brought out to the lawn and used to spell a seriously profane salutation.

Despite all its amiable qualities, however, “Salad Days” never quite overcomes its defects, the most serious being that this is a 412-page book that takes us only through the author’s 32nd year, which means that a lot of time is spent on events of very little moment. Also, though Fairbanks’ tone throughout is quite self-deprecatory, though he is more than willing to apologize for all the times he was “an affected, infatuated young ass,” that does not make all those times any easier or more edifying to read about.

The book’s biggest flaw, ironically enough, is visible in its most involving sections, when Fairbanks talks about the two people he felt most strongly about, his father and his first wife (married when he was 19), the once and future Joan Crawford. Fairbanks stands in frank awe of Doug Sr., the most vibrant of characters off as well as on the silent screen, and Crawford, the ultimate in self-willed, self-created stardom, and well he might. For they both have key qualities that he lacks--an intensity of feeling, a vibrant emotional willfulness. Without that, no matter how many famous folks Fairbanks found favor with, his salad days inevitably come up lacking in vinegar.