For example England has "HMS", the United States "USS" but I have been trying to find the Soviet Union's ship prefix and cannot find anything, did they simply not have a ship prefix?
No, they did not have an official ship prefix (which is not completely unusual -- the Imperial Japanese Navy and Kriegsmarine both did not, although authors will sometimes add prefixes to ship names to identify them.)
You will sometimes see Soviet ships referred to as "USSRS", although a literal transliteration using Cyrillic would be KCCCP -- the acronym would be for "Корабль Союза Советских Социалистических Республик," "ship of the Union of Soviet Socialist Republics."