No law requires it
Federal law doesn't require paid holidays, and it doesn't require extra pay for working one. A holiday is an ordinary workday under the FLSA. Whatever premium you get comes from your employer's policy or a union agreement, which is why the multiplier here is a choice, not a fixed rule. Most employers that pay a premium use 1.5x; some use 2x for the biggest holidays.
Holiday pay and overtime
Paid time off for a holiday you didn't work doesn't count as hours worked, so it doesn't push you toward the 40-hour overtime line. Eight paid holiday hours plus 36 hours worked is 44 hours of pay but zero hours of overtime. Hours you actually work on the holiday do count. Check a week like that with the overtime calculator.
Holiday plus overtime in one day
If a holiday shift also takes you past 40 for the week, most policies pay the higher of the two premiums, not both stacked. Some union contracts do stack them. Read the clause, then use the double time calculator if the answer is 2x.