Is it true that is gollum in the fellowship of the ring based on the following text?

The Fellowship of the Ring, the first volume of The Lord of the Rings, explains that Gollum's real name was Smeagol, and he had once been a member of the secluded branch of the early Stoorish Hobbits. He spent the early years of his life with his extended family under a matriarch, his grandmother. On Smeagol's birthday, he and his relative Deagol went fishing in the Gladden Fields north of Lothlorien. There, Deagol found the Ring in the riverbed after being pulled into the water by a fish. Smeagol fell immediately under the Ring's influence and demanded it as a birthday present; when Deagol refused, Smeagol strangled him. Smeagol later used the Ring for thieving, spying and antagonizing his friends and relatives, who nicknamed him ''Gollum'' for the swallowing noise he made in his throat, until his grandmother expelled him from the family. He wandered in the wilderness for a few years until he finally retreated to a deep cavern in the Misty Mountains. The Ring's malignant influence twisted his body and mind, and prolonged his life well beyond its natural limits.

Possible answers: a. no; b. yes;
b.