The correct name of the following polymer is:

• Repeating Unit: The backbone consists of a repeating chain unit featuring a quaternary carbon bonded to two methyl groups ($$-\text{CH}_2-\text{C}(\text{CH}_3)_2-$$).
• Monomer Identification: This polymer is formed via the addition polymerization of isobutylene (2-methylpropene, $$\text{CH}_2=\text{C}(\text{CH}_3)_2$$).

Conclusion:

Polymerizing isobutylene monomers results directly in polyisobutylene.

Answer: Option A — Polyisobutylene