The approximately 10 million aliens living in the United States will not have to report their names and addresses to immigration authorities this month as they have for the past 30 years.

An amendment to the Immigration and Nationality Act, signed by President Reagan Dec. 29, removes the annual reporting requirement. Immigration and Naturalization Service officials point out, however, that aliens are still required to notify the INS within 10 days whenever they change their address.

"It's a relief. . . . It was a burdensome thing to do," said INS spokesman Duke Austin of the annual reporting requirement. By eliminating the requirement, the INS will save $1.2 million a year and save some duplication of paperwork, he said.

Last year, Austin said, INS printed 18 million postcard reporting forms and sent them out to post offices and INS regional offices for aliens to fill out.

Some 5.3 million aliens sent in cards, but an unknown number of others, many of them illegal, did not. The Census Bureau estimates there are 3.5 million to 6 million illegal aliens.

Austin said the postcards had to be processed by hand rather than by machine, thus increasing costs and the burden. Also, most of the aliens who complied with the reporting requirement notified INS of address changes anyway.

He said the amended law permits the attorney general to reinstitute some form of annual reporting if he feels it necessary.