Crossover's primary menus in Ubuntu's Unity window manager are confusing because Crossover actually has a series of launcher items, none of which are named "Crossover". In other menu systems there's a Crossover category to contain these launchers, but in Unity this isn't working, yet. So, if you search for "Crossover" after installing the program, all you'll find are files, installer packages, and folders.
Clicking on these icons will not launch the Crossover program, itself (and will probably just create an even more confusing situation if you end up trying to re-install).
Crossover's normal menu icons are actually present, but they're listed in alphabetical order by the name of the menu item, rather than by "Crossover".
The menu items are as follows:
"Install Windows Software"
"Register and Unlock this Demo" (trial, only)
You can find each of these by searching for the name, as above, or by looking in your list of "All Applications" in Ubuntu's Applications menu, where you'll find them in alphabetical order.
Note that your installed Windows Applications launchers will obey the same rules - they're listed in alphabetical order under All Applications
You can save Crossover's menu icons in your side launch bar just as with any other program, but you will have separate icons for each menu item, rather than one blanket Crossover icon. Mousing over the icons you've saved will show their name: