Rampton, 93, is the only governor to serve three full terms, beginning in 1965. He has been in hospice care with inoperative cancer since July, according to family members.
"When future generations of state leaders enter this boardroom, the inspiration of a great leader will accompany them," said Republican Gov. Jon Huntsman Jr. "Governor Rampton's example is one we can all emulate and, to the extent we do, we will be better and more effective. He was a powerful statesman."
During January's legislative session, leading lawmakers plan to sponsor a resolution making the change.
Senate Minority Leader Mike Dmitrich, D-Price, said Rampton called for the first statewide bond to build and improve the state's college and university buildings. "He modernized state government to function as it does today," Dmitrich said
House Speaker Greg Curtis, R-Sandy, said Rampton was a "giant" of Utah history.
"When Governor Rampton believed in something he would follow through," Curtis said. "He was a tough, progressive governor, and he was a true visionary."
Though the Rampton Boardroom will be equipped with state-of-the-art communications, its fixtures, drapery, painting, carpet, and furnishings will be historically accurate to 1915 when the Capitol was built.
The restored and earthquake-protected Capitol will reopen for the January session.


