If you do not know the name of a knot, KnotFinder can help you. From the diagram of the knot, find its DT notation. Enter the DT code and click "Find." For now, KnotFinder finds only prime knots with crossing number 13 or less.
KnotFinder is powered by KnotScape, but gives the classical Name of the knot, rather than the DT Name returned by KnotScape.
Other, more up-to-date knot indentification tools can be found elsewhere online, such as these. (Use at your own risk!)
Knot identification can also be done with the programs SnapPy, KnotPlot, and KnotScape.