Question

Do astronomers have another name for our moon?

Answer 1

No. Officially, it is only “Moon”

Explanation:

Officially, it is only “Moon”.
See the following page for UIA definitions:
https://www.iau.org/public/themes/naming/

As a part of larger society, astronomers probably also use common variants or historical labels in conversation. But for scientific astronomic usage is it only the Moon.

Here is a recent light-hearted look at the issue as well:
http://www.universetoday.com/120087/what-is-the-moons-real-name/