I have read that Genghis means "Ocean."
If not true, what does it mean?
And if true, does it mean something like 'from one ocean to the next' or along the lines of 'khan of the great grass ocean'?
It does mean 'ocean' like you said you have noticed, but when you combine Genghis, which is 'ocean', and Khan, which means 'ruler', you end up with a meaning of "universal ruler." Historians are still unsure of the exact origins of the word "Genghis", but they do concur that "universal leader" is what is implied with "Genghis Khan." This is a useful source to learn more: http://www.history.com/news/history-lists/10-things-you-may-not-know-about-genghis-khan