You can't use a celebrities name or likeness on any merchandise without permission.
It's called the "right to publicity". Meaning, the celebrity (or whoever actually) has the right to decide how their image and name is used commercially.
As posted above, politicians are exempt from this "right to publicity" rule for some reason. That's why people can get away with selling Arnold Schwartzenegger t-shirts (as long as they are related to him being governor of California).
How in the heck does SNL get away with mocking anything in sight and profiting from it?
It could be that he has permission or it could be that they already went through a legal process and had a precident set. Or, it could be that since SNL is so big, it's almost extra PR for a celebrity to be featured or parodied there. No way to tell without talking to SNL I guess
