Pharaoh's Daughter / Naming of Moses

1. Yered (ירד), implying descent. According to one opinion, Miriam gave him this name, for because of him, she went down (yarad) to the Nile to see what would become of him. Alternatively, Moses was called this name because he brought the Torah down to the Jewish people, and the Divine Presence back down to this physical world.
2. Avigdor (אבי גדור), master of the fence. According to the Yalkut Me'am Loez, he was called this (by his grandfather, Kehat), because "since Moses' birth, G‑d has fenced in Pharaoh, not allowing him to continue his decree to drown Jewish infants."
3. Chever, (חבר) meaning, companion, or connector. Either because Moses connected the Jewish people with their heavenly Father, or because he prevented Heavenly retribution for their sins. Some say that Amram, his father, gave Moses this name, because Moses was born after his father had once again joined his wife after having divorced her.
4. Avi Socho, (אבי סוכו) Father of Seers. He was given this name by his grandfather, Kehat (alternatively, by the nurse who helped Moses' mother raise him), because Moses would grow up to be the "master" (avi) of the seers (sochim) and prophets.
5. Yekutiel (יקותיא-ל), from the root kavei (קוה) meaning hope. His mother Jochebed called him this name because she had hope and trust in G‑d that He would return Moses to her. Alternatively, because she foresaw that Moses would be the Jewish nation's great hope.
6. Avi Zanuach (אבי זנוח), literally, "master of rejection." Aaron, Moses' brother gave him this name, saying "My father rejected my mother, but took her back because of this child." Alternatively, because Moses would make Israel reject idols.
7. Tuvia (טובי'ה), implying goodness.
8. The Jewish people called him "Shemaya (שמעי-ה) ben [the son of] Nethanel." They predicted that in his days, G‑d would hear (שמע) their prayers.
9. Ben Avitar (בן אביתר), son of pardon, since Moses was the Jewish son who would solicit G‑d's pardon (ויתר) for the Jewish people's sin of the Golden Calf.
10. Levi (לוי), so named after the tribe to which Moses belonged.
(Source: Rabbi Eliezer Danzinger, Chabad.org)