Quote from Tag-MehirTzedek
Then if Yocheved or someone else known the name(s) why weren't they using it when they saw others afflicted and even killed? If you say its forbidden then what would have allowed Moshe to do soo then.
In Kol Hator, the disciples of the Vilna Gaon claimed they had received secret names of G-d to help them above natural means but were forbidden to use them except to prevent a desecration of G-d or to save the Yishuv in the land of Israel.
Maybe Moshe felt the situation in front of him was needed to prevent a desecration of G-d.
Possibility #2, I have heard that if people who are on too low a spiritual level use these names it can bring disaster upon the user. Moshe felt he was on the level to use them.
I heard a rumor that an important rabbi blamed his use of Divine names for a terror incident that befell his family. Since I don't have sufficient verification for the story I will not provide further details.
Possibility #3 According to Maharal's Gur Aryeh commentary on Rashi, in order for the Divine names to work against the Egyptian it had to be accompanied by some type of physical hitting of the Egyptian. The Divine name magnified the small weak hit into a powerful hit that was strong enough to kill the Egyptian. So according to Maharal even if other Jews had the knowledge of the Divine names, it wouldn't work for them as long as they were too scared to give the Egyptians even a weak hit.