The First Battle was fought when Morgoth sent two armies of Orcs down into Beleriand, one in the west and one in the east, in a time before the Return of the Noldor.
(1)
The eastern army pushes southwards and defeats the Laiquendi at Amon Ereb, slaying their leader Denethor.
The eastern Orcs are finally defeated north of the Andram, and flee back towards the North.
(4)
The fleeing remnant of the eastern army of Orcs is set upon by Dwarves out of the Blue Mountains, and almost completely destroyed.
(5)
The western army of Orcs is almost unopposed. Driving Círdan into his Havens, elsewhere they roam freely through West Beleriand.
The First Battle was fought when Morgoth sent two armies of Orcs down into Beleriand, one in the west and one in the east, in a time before the Return of the Noldor.
(1)
The eastern army pushes southwards and defeats the Laiquendi at Amon Ereb, slaying their leader Denethor.
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 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.