President Reagan has ordered the name of the Navy attack submarine Corpus Christi changed to City of Corpus Christi following protests by church groups, several members of Congress and a radical Christian activist conducting a two-month hunger strike here.

"The president felt the original name could be offensive to Christians," a White House spokesman said yesterday. Corpus Christi means "body of Christ" in Latin. Many church leaders objected to giving the name to a warship.

In February, Mitch Snyder, a member of the Community for Creative Non-Violence here, said that he had begun a water-only fast as a protest.

Last Thursday, House Speaker Thomas P. (Tip) O'Neill (D-Mass.) telephoned White House deputy chief of staff Michael K. Deaver, saying the name, Corpus Christi, was inappropriate.

Deaver spoke to the president, who agreed.

Earlier, Navy Secretary John Lehman sent an emissary to Snyder. Navy spokesmen denied the visit was designed to seek a compromise, but Snyder said the emissary, Navy attorney Hugh O'Neill, asked if adding the words "City of" to the name Corpus Christi "would be okay."

"I told him, yes, it would; it would secularize the name," Snyder said, adding that he would end his 63-day fast.