According to the information I have read, the term "Navy" was a term used by Mr. Colt to describe the .36 caliber pistol and had little to do with what the Navy liked to use.
It may have had ties to the Texas Navy being armed with the .36 caliber Paterson Colt pistols during the Texas Navy vs the Mexican Navy battle on May 16th, 1843.
Quoting from page 50 of COLT AN AMERICAN LEGEND by R.L.Wilson,
"Colt seems to have introduced the term "Navy Model" to firearms nomenclature. His intent apparently was that the Dragoon would sell for the Army service, and the Navy type for the sea. However, most of the '51 Colts sold to the U.S. government were designated for military, not naval, use. The first U.S. contract purchase of the '51 was for 1,000 specimens, in July 1855. Many thousands more were sold for service use there-after..."