The title of this article is conjectural. While the content of this article is based on official information, the actual name of the subject is conjectural, and is yet to or cannot be officially named.
The island was made of rock and lay in the center of an underground lake. According to The Atlas of Middle-earth, it was between 150-200 feet from the lake's western shore, near the entrance to the tunnel. From here Gollum had good visibility and could see to the other side and could quickly paddle to and from the island in his little raft.
As Gollum's home it was no doubt where he slept and possibly where he stored things taken from his goblin victims. The most valuable thing he stored here was his Golden ring; his "Birthday Present" his "Precious", which was hidden in a hole in the island's rock when he wasn't wearing it.
Gollum abandoned his slimy island when he left the cave a few years later to search for the ring and the thief Baggins.