Does the word gymnastics come from the greek word naked?

Unfortunately, yes.

Gymnastics is ultimately derived from the Ancient Greek Word gymnos, "naked".

That Word became gymnazien "to exercise or train", or literally "to train naked". This in turn became gymnastikos"fond of or skilled in bodily exercise", and was translated into Latin as gymnasticus.

Gymnastics, as we know it today, was actually known as gymnastic as early as the 1570s. In the 1650s, however, the revival of the classical -ikos Greek ending as -icsturned gymnastic into the modern gymnastics.