You may not use God's name unless there is a positive purpose. Anyone may say any of God's names anytime when studying Torah, even a girl or woman who is reading the Torah with cantillation/trop where she might need to repeat God's name or other words in a line/pasuk and thereby not say the entire pasuk as it is written.
It is permissible to use God's name (and not an altered name such as “Keil” or “Elokim”) in these cases:

• When reciting a sentence or phrase from the Torah.
• For any type of teaching of Torah, blessings, and prayers to children up to bar/bat mitzva age.
• In Shabbat songs/zmirot.