Many analysts have one, but it is not always required. Employers look for evidence that you can investigate: labs you have completed, write-ups you have published and certifications such as Security+.
Is SOC work only night shifts?
Some SOCs run around the clock and use shifts, especially at managed security providers. Many in-house teams work business hours with an on-call rotation.
How is this different from a penetration tester?
An analyst defends and investigates live systems. A penetration tester is hired to find weaknesses before attackers do. The skills overlap, and many people move between the two.