After a wrenching five-month search for the perfect name, the company that will take over local telephone service in the District and six mid-Atlantic states next year decided that "Bell Atlantic" had a nice ring to it.

Bell Atlantic will be one of the seven regional operating companies formed when American Telephone & Telegraph Co. divests itself of its local telephone companies next year as part of a Justice Department anti-trust settlement.

Naming these new telephone offspring of Ma Bell has challenged some of Madison Avenue's costliest wordsmiths--with some strikingly different results.

Bell Atlantic, the new name for the company formed by the six Bell mid-Atlantic state telephone companies plus the District's Chesapeake and Potomac Telephone, was hardly a creative leap, for example.

To help select and test-market the new name, said a Bell Atlantic spokesman, the company called in Landor Associates, a New York-based firm with a track record in corporate christenings. Landor had handled Allegheny Airlines' metamorphosis to USAir.

"What Bell Atlantic needed was a name appropriate to an $18 billion corporation," said Robin Thompson of Landor. The difficulty, he said, was that "our research showed that a lot of people wanted to say two contradictory things: on one hand, they wanted to be seen as a new company; on the other, they wanted to preserve the stature and heritage of a major corporation."

Not coincidentally, Thomas E. Bolger, the designated chief executive officer of the company, had wanted to keep the Bell name.

The Bell Atlantic moniker runs awry from the high-tech names chosen by some of the other regional operating companies. The midwestern regional company decided it liked the rhythm of "Ameritech." The northeastern region opted for the cacaphonious NYNEX. "It's an acronym based on New York Telephone and New England Telephone," said Bruce Pulling, NYNEX's vice president of administration, adding that a consultant was called upon for advice. "The 'X' means our opportunities are unknown and unlimited."

Pulling said the company did not test-market the name.

A Bell Atlantic spokesman said that its search for a new name cost "well under a million dollars" and that the company was very satisfied with the result.