PR giant Sonnenberg, the subject of new biography; Always Live Better Than Your Clients, by Isadore Barmash. New York: Dodd, Mead & Co. 208 pp. $15.95.

Benjamin Sonnenberg was publicist, press agent, public relationist extraordinaire. He wove fantasies for corporations, made the obscure famous, and put millions in his own pockets doing it.

Representing company giants like Juan Trippe of Pan American World Airways Inc. and Charles Luckman of Lever Brothers, Sonnenberg built up his own image to tower over all other myths he created. With spats and twirling cane, the entrepreneur strutted through the imagination of anyone who hired him.

Isadore Barmash, business writer, ignored the late Sonnenberg's expressed wish that no biography be written about him. And well he might. With a fascinating story to tell, Barmash decided that the man whose public life was an open book, should be depicted in one.

Barmash tells the story of the East Side Russian immigrant intensely curious about how the other half lives. With unusually mature vision, the young Sonnenberg ''. . . took a tintype in my mind of the way I wanted to be - a bon vivant, and patron of the arts, a man who could mix Picasso with Dun and Bradstreet.''

With self-assurance and a cocky philosophy (''always live better than your clients''), Sonnenberg never groveled for business. Instead, corporate moguls flocked to his 37-room Gramercy Park mansion to ask for his services. They dined amid English antiques, were entertained by films furnished by Samuel Goldwyn in ''the house that hot air built,'' as Damon Runyon called it.

With zest, Barmash unveils both the public Sonnenberg, who scattered simulated gold dust on New York streets to advertise Bergdorf Goodman's, and the too-busy father who never succeeded in impressing his own son. Sonnenberg possessed a secret, it seems, that sent his creative genius soaring above other publicists: his pizazz was exceeded only by his chutzpah.