Mormon was a person, (they named the book after him), and the LDS church does not follow a person, they follow God (And Jesus).
Mormon is a nickname that was given to them because of the name of the extra book they had called "Book of Mormon" the name of their church is precise "Church of Jesus Christ of Latter Day Saints"
while in my experience they haven't taken any offense to being called Mormon, I always try to use the term LDS, I believe that it is more correct than Mormon.
Mormonism implies Cult, which is a touchy subject.
I as a non-denominational Christian would say that they are not a Cult, because I believe we would have to classify other religions as Cults as well.
I wouldn't use the term Mormonism because right away someone who doesn't know anything about the religion would instantly think "Cult", and I prefer not to help other people judge a large group of people.
If I were still Mormon/LDS I would prefer to be called an LDS Member or Latter-day Saint. Mormon wouldn't bother me, but I would prefer something more formal.