A Covered Call consists of a stock position and a call option position. If you hold the underlying stock and short the corresponding call option, you have created a Covered Call strategy.
It should be noted that the number of shares of stock position must be the at least the same as the number of shares implied by the option contract size. In other words, if you short a call option of company ABC, and the contract size of that option is 100, then you need at least 1 * 100 = 100 shares to form a Covered Call strategy.
The option contract size of most US stock options is usually 100.
Generally, margin requirements for Covered Call position is lower. Margin is only required for the underlying stock position in a Covered Call strategy, waiving the margin requirements for the option position. When you hold the underlying stock and place an order to sell an option contract, no margin is required for this option order and therefore will not impact your purchasing power.
Same as account financing, option strategy margin reductions are subject to internal risk control parameters. If your short call option margin is not reducted, the reason may be that you do not hold enough underlying stocks, have orders to sell the stocks, or have exhausted your margin reduction quota.