The day belonged to Dr. Loyal Davis, the eminent American neurosurgeon who yesterday added an honorary fellowship in the Royal College of Surgeons in Ireland to his list of glittering professional accolades.

He was upstaged, though, and hardly seemed to mind.

"You know," said one of the physicians who attended Davis' son-in-law during a recent hospitalization, "Dr. Davis is here on his own ticket."

There had been no presidential election in this country and Davis' stepdaughter and son-in-law had not yet moved into the White House when the Royal College decided to confer its highest academic honor on Davis, who is retired, at 85, from active practice. And the induction was supposed to have been in Dublin.

Instead, it turned out to be a major White House production yesterday afternoon at the Irish Embassy. There was an eclectic mix of some of the major surgical greats in this country and in Ireland, a retinue of TV cameramen, Secret Service, White House aides, embassy aides (with lilting brogues) and even a delegation from Bloomingdale's (including chairman of the board Marvin Traub), which is planning a big Irish do in the fall. There was also a Cabinet member with an Irish name (Labor Secretary Raymond J. Donovan), and another without -- HHS Secretary Richard Schweiker.

Davis, his frail wife -- the first lady's mother -- by his side, wearing a brilliant red suit and seated in a wheelchair, pledged as required by the college (and with a trace of a twinkle) that "I am 25 years of age and upwards" (and, among other things, pledged that he is not now and will never be a practitioner of "the business or profession of an apothecary, or druggist . . .").

But inevitably it was his son-in-law the president and First Lady Nancy Davis Reagan who claimed the lion's share of limelight, the first lady in a cool, white lawn dress with embroidered bodice, the president looking so well and vigorous that even Dr. Dennis O'Leary seemed awed.O'Leary, the world's link with the president as he lay wounded in the George Washington University Medical Center last spring, drew a double take and the warmest greeting of the day from the Reagan's. A pleased Margaret O'Leary, who had seen less of her husband during that time than had the Reagans -- than had, in fact, the TV-viewing public -- received "a gracious thank you" from Mrs. Reagan. So did O'Leary. "Are they taking good care of him?" he was asked.