I recently started taking a class. There is a "get to know you" discussion forum that we are all supposed to participate in. Is there a good reason I should refrain from mentioning my specific place of employment?
There is pretty much no downside to telling people where you work. You are not revealing any confidential secrets, and it's extremely unlikely that anyone can use the information against you.
Exceptions might be if you are deeply embarrassed about where you work ("yourbestporno.com") or you work for a secret intelligence agency (not out of the question - I knew several people who worked for GCHQ and AWE and they tended to introduce themselves as 'working for a government laboratory'). Conceivably if you worked for a stealth mode startup where your interests might give away the company's program.