He was named for the sound he made. It was a sort of 'gollum' sound deep in his throat.
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He got the name from the sound he made in his throat. His name before The Ring corrupted him was Sméagol.
Sméagol was Gollum's original name.
Frodo already knew that Gollum was Smeagol because Gandalf told him earlier in the Fellowship of the Ring. When Gollum hears his old name, he realizes who he really is and that his master Frodo is the one who takes care of him now and no longer needs "Gollum".
His name is Gollum.
Bilbo said, talking to himself, "what have i got in my pocket?" (it was the Ring). Gollum thought it was a riddle and Bilbo decided to make it one. he gave Gollum three chances to guess and gollum lost after four. then gollum went "to get something" (it was the ring), and Bilbo thought he was abandoned and left with the ring on. Gollum thought Bilbo knew the way out and he wanted to follow him, realizing Bilbo had the ring. Bilbo saw Gollum racing towards the gate and followed him to safety.
His name was Gollum and he was a Hobbit that was corrupted by the magic of the ring that he carried for the extended period of time before it fell to the hands of Frodo and the Fellowship of the Ring.