President Reagan announced yesterday that he will send the names of his 10 nominees to the board of directors of the Legal Services Corp. to the Senate for confirmation.

Six of the appointments are controversial because Reagan made them on New Year's Eve while Congress was not in session, which enraged some of the legal services community.

A number of former board members filed suit in U.S. District Court here yesterday charging that the New Year's Eve appointments were illegal and asking the court to prevent the new board from taking any formal actions before they are confirmed by the Senate. The administration contends that the recess appointees could legally serve without Senate confirmation until the end of the current congressional session.

The Reagan board has scheduled a meeting for next Friday.

Some corporation staff members say they believe the recess appointments were made in an attempt by the Reagan administration to block the quasi-governmental agency from making $224 million in grants to local legal aid offices for this year. However, by the time Reagan made the appointments, the previous board had already signed contracts for the programs all over the country and the first two months of funding had already been sent out.

Reagan says he plans to abolish the corporation, but Congress has refused to go along with it so far.

Nominees to the board were identified by the White House as:

Howard H. Dana Jr. of Cape Elizabeth, Maine; Harold R. Demoss Jr. of Houston; William L. Earl of Coral Gables, Fla.; William F. Harvey of Indianapolis; Clarence V. McKee of Washington; William J. Olson of Falls Church; George E. Paras of Sacramento, Calif.; Marc Sandstrom of La Jolla, Calif.; Annie Laurie Slaughter of St. Louis, and Robert Sherwood Stubbs II of Waleska, Ga.

Dana, Harvey, Olson, Paras, Sandstrom and Stubbs are the New Year's Eve appointees.