LEAD: There has almost never been a Philadelphia without a Rittenhouse. The name calls forth images of old money and low-key gentility.

There has almost never been a Philadelphia without a Rittenhouse. The name calls forth images of old money and low-key gentility.

Rittenhouse Square, one of four eight-acre public parks set aside when William Penn laid out the city, is at once a symbol of the city's past glory and an elegant, leafy oasis of throbbing late 20th-century urban humanity. Business after business in the surrounding neighborhood of town houses and skyscrapers basks in the reflected cachet of a name everybody knows, or has at least heard of: Rittenhouse Psychology Group and Rittenhouse Cleaners and Tailors, and so on, through 39 lines in the telephone book.

But who really were the Rittenhouses and what do they represent? Not even all those who bear the name have always been entirely sure. ''I always knew Rittenhouse Square was there, but I didn't know what it meant,'' said Jennifer Rittenhouse, 24 years old, who lives just north of here in the town of Blue Bell.

In this season of family reunions, Ms. Rittenhouse and more than 400 of her clan of 40,000 to 50,000 blood relations converged this weekend on Philadelphia from 26 states and Canada to explore and re-illuminate the family heritage. It was a time of reawakening and in some cases rediscovery, the first Rittenhouse reunion in nearly a century and only the second in 300 years.

Three centuries ago this year, just six years after Philadelphia's founding, the first Rittenhouse came to America. He was William Rittenhouse (Wilhelm Rittinghausen in his native Germany), and he came here as did so many others of his age to find economic opportunity and religious tolerance.

He was the first Mennonite minister in America, and he established its first paper mill, in what is now Fairmount Park. It produced most of the American-made paper of the Colonial and Revolutionary periods. Rittenhouse paper went into not only Revolutionary tracts but also into cartridges and gun wadding for the Continental army.

The whitewashed stone buildings of the original Rittenhouse homestead, restored and spruced up, are nestled in RittenhouseTown, along the banks of a tumbling brook in a secluded, thickly wooded enclave in the middle of Philadelphia. This afternoon the patriarch's descendants gathered there for a box lunch, a short play and the sharing of memories.

This weekend they ate, drank, pored over genealogical books and charts, listened to lectures about their ancestors and decided to set up a permanent family organization. In the words of Harold R. Rittenhouse of Harleysville, Pa., the organizer of the tricentennial reunion, they ''reasserted family ties.''

It was David Rittenhouse, the patriarch's great-grandson, who is perhaps most responsible for the name's luster. He was a contemporary of Benjamin Franklin and was born at RittenhouseTown, became a clock maker and an astronomer and was deeply involved in the Revolutionary movement. Rittenhouse Square was named for him in the 19th century.

Although many of the city's movers and shakers lived around Rittenhouse Square in the late 19th and early 20th centuries, few, if any, were Rittenhouses. Milton Rubincam, a genealogist and an authority on the family who spoke at the reunion, said that while many in the family have distinguished themselves in given fields over the years, they have generally not been part of Philadelphia's industrial-age ruling elite.

Rather, as is true with most American clans, they have spread across the continent and throughout the walks of life. Harold Rittenhouse, for instance, is a real estate broker. His distant cousin, Jennifer, who coordinated arrangements for the reunion, is a pharmaceutical sales representative. Kirtland G. Smith, who came to the reunion wearing a T-shirt proclaiming his Rittenhouse lineage, is a stockbroker from Seattle.

''It's a pretty diverse group,'' Mr. Smith said. ''Over 300 years you're bound to get that kind of diversity.''

Why do people come to such a reunion? Pride, surely. But also, said Jennifer Rittenhouse, ''I think people are searching more for their identity now, becoming more aware of themselves and wanting to put into perspective where they've come from.''

Ms. Rittenhouse is the daughter of a farmer, and schoolmates used to call her Jennifer Chickenhouse. ''I used to get angry at being teased and having to write such a long name,'' she said.

But today, she said, ''people ask, 'Are you related to the Rittenhouses of Philadelphia?' and you say yes, and it's really a nice feeling. You feel special.''