Unity Bank & Trust Co. in the Roxbury section of Boston, the only minority-owned bank in all of New England, today got a new new name, new capital and new black management.

The failed bank, which has been run by a conservator since 1971, is now the Boston Bank of Commerce. The 7,200 depositors in the old bank move to the new one, which was made possible by a $6.1 million advance from the Federal Deposit Insurance Corp.

The president of the new bank is Juan Cofield, a Wharton School graduate who worked for Bankers Trust in New York. He and his brother run a real estate finance company in Boston called Malmart Corp.

Gerald T. Mulligan, the Massachusetts banking commissioner, says that Unity was not given special treatment because of its minority status. "There was bidding for the bank, and Cofield's was the winning bid," he said.

There are 95 minority-owned banks in the country, according to the Federal Reserve Board. Under the minority bank deposit program, federal agencies have been encouraged to use minority institutions for their banking needs whenever practical since the program was introduced in the Nixon adminsitration. The Reagan administration has not endorsed the program, however.

Since 1971, about a dozen minority banks have failed, according to a Fed official.

Unity's problems were typical of those that plague many minority-owned banks: inexperienced management, weak loans and poor customers. The bank was founded in 1968. By 1971 Unity's $1.2 million in capital had been dissipated by bad loans. That year, the FDIC wrote a six-year, $1.5 million capital note, and four major Boston banks invested $500,000 in the bank's recapitalization.

But by 1977 the bank couldn't make the payment, so the funds from the banks and FDIC were rolled over for another 5 years. By June 30 of this year, the bank again couldn't make the payments and was declared insolvent.

The $6.1 million FDIC advance to Boston Bank of Commerce includes the $1.3 million advanced in 1971 plus most of the $500,000 that was not repaid to the Boston banks.

Commissioner Mulligan says he hopes that so-called "conscience money" will flow to the bank from the Boston area's many corporations, trusts and educational institutions. Because of its constant liquidity problems, Unity was never able to market itself, says Mulligan.

Unity's loan portfolio was concentrated in Roxbury, a poor black section of the city. The new bank hopes to spread its loans to corporations as well as individuals. It plans a new downtown branch to help broaden its customer base.

Mulligan says the new bank has "an impressive group" of board members lined up. A state agency, the Community Development Fund Corp., invested $800,000 in preferred stock.