Beren's dates were subject to several revisions, and the full details of his birth and death are unclear. The dates given here are taken from various sources in volume XI of The History of Middle-earth, especially The Grey Annals and The Tale of Years. Beren's date of birth is particularly uncertain; it is given as I 432 in a genealogy of the House of Bëor, but the other dates from that source were revised (in some cases several times), so it is far from certain whether this date was intended to stand.
2
At least, according to the The Etymologies. (The History of Middle-earth volume V, The Lost Road and Other Writings III The Etymologies). Beren seems to have a taken his name from his grandfather, the father of his mother Emeldir, who was the first of his House to use the name Beren.