vefanyar:

But Galadriel did not depart from Doriath, and remained long with Melian, for there was much love between them. […] And at times they would speak together of Valinor and the bliss of old; but beyond the dark hour of the death of the Trees Galadriel would not go, but fell ever silent.

And on a time Melian said: ‘There is some woe that lies upon thee and thy kin. That I can see in thee, but all else is hidden from me; for by no vision or thought can I perceive aught that passed or passes in the West: a shadow lies over all the Land of Aman, and reaches far out over the Sea. Why wilt thou not tell me more?’

‘For that woe is past,’ answered Galadriel; ‘and I would take what joy is here left untroubled by memory.’

aredhels:

It is said that though called Nerwen by her mother and Artanis by her father, the name she chose to be her Sindarin name was Galadriel, “for it was the most beautiful of her names, and had been given to her by her lover, Teleporno of the Teleri, whom she wedded later in Beleriand.