* The Moon doesn't have its own sunrise. The Moon doesn't produce light; it reflects sunlight. So, while we see the Moon illuminated from the Sun, there's no "rising" or "setting" of the Sun on the Moon's surface the way we experience it on Earth.
* The Moon's rotation and orbit are synchronized. The Moon rotates on its axis at the same rate it orbits the Earth. This means the same side of the Moon always faces us. From the Moon's perspective, the Sun would appear to move across the sky over a much longer period (about a month), instead of rising and setting each day.
So, to answer your question more directly:
* The Sun would appear to rise in the east on the Moon, just like on Earth, but this "sunrise" would be a much slower process.
Let me know if you have other space-related questions!