First Battle

The text of The Silmarillion is not specific about the date of the First Battle, but the Grey Annals (in volume XI of The History of Middle-earth gives us a definite date. That date is Valian Year 1497, which translates to about 29 (solar) years before the first rising of the Moon and Sun. To put this into perspective, Morgoth had returned to Angband about twenty years beforehand, and the Noldor would follow him into Middle-earth about seven years after the First Battle. (Valian Years were rather longer than solar years, so all the figures given here are necessarily approximate conversions.)

The lack of any alternative name for the First Battle is notable, because it breaks an otherwise regular pattern: from the Second Battle onwards each of the numbered battles of the Wars of Beleriand carried its own distinctive title. So, the Second Battle was the Dagor-nuin-Giliath, the Battle-under-Stars; the Third was the Dagor Aglareb, the Glorious Battle, and so on.

The reason for the missing name seems to relate to Tolkien's development of this idea over time. In the original scheme, the numbered battles started with Dagor-nuin-Giliath as the First Battle, not the Second. This scheme was later expanded to include Morgoth's invasion of Beleriand before the Return of the Noldor, which was now explicitly the First Battle of the Wars of Beleriand, but this new inclusion never received its own independent name.