Dictionary of Alaska Place Names by Donald J. Orth, United States Government Printing Office, Washington, reprinted 1971, page 279, indicates there is a Dome Creek, which is a stream that flows NW 7 miles to Chatanika River, 16 miles north of Fairbanks. Local name derviced from Pedro Dome located at head of stream. Name first reported in 1903 by T. G. Gerdine, USGS.
There are lots of Dome Creeks in Alaska but this appears to be the one closest to Fairbanks.
page 746 indicates that Pedro Dome is a mountain, 2600 feet high, 15 mmile NE of Fairbanks. Local name derived from Pedro Creek, reported in 1903 by T. G. Gerdine, USGS.