KnotFinder is a web page, powered by Knotscape, that takes as input the DT notation of a knot and returns the DT name of the knot. (The knot table is ordered by classical names for knots of fewer than 11 crossings, but also gives the DT names.) KnotSketcher, now under development by Jiho Kim, lets you draw a knot and returns the DT notation. It requires Java 1.4 to run, and make take a minute to start up.
If KnotSketcher does not run on your computer, you can still use Knot Finder. Just find the DT notation of your knot and enter it into Knot Finder.