You will find a database listing the Liberty Ships by name, with an indication of type of vessel, at this link. It is part of a site devoted to Liberty Ships posted by Peter Thompson of Florida International University.


Another page from the site contains this summary of the numbers:

"The standard Liberty ship, an all-welded cargo ship with a displacement of 7,000 tons, was the centerpiece of this program. ... Eventually, 16 U.S. shipyards delivered a total of 2,580 Liberty ships ships, by far the largest ever production run of the a single ship design. An additional, 119 Liberty ships were produced with modified designs -- colliers, tankers and and aircraft and tank transports -- were also delivered."

See Professor Thompson's article: "How Much Did the Liberty Shipbuilders Learn? New Evidence for an Old Case Study." Journal of Political Economy, 109(1):103-137