The Elvish name for Lothlórien was Laurelindórenan but it was made shorter perhaps because the forest was fading and not growing. Meanwhile, the origin of the name 'Lórien' is derived from 'Lothlórien', which makes it a further derivation of 'Laurelindórenan'.
Interesting tidbit
Following the departure of Galadriel for Valinor at the beginning of the Fourth Age, the Elves of Lothlórien were ruled by Celeborn alone, who led them across the Anduin to found a new, larger realm, East Lórien, centred around Amon Lanc. By the time of the death of Queen Arwen, Celeborn and Galadriel's granddaughter, Lothlórien itself was deserted.