MCI Communications Corp., a long-distance telephone company that has grown into a $500 million business largely because of its advertisements promising bargain rates, is about to raise rates for most customers in the next two months, MCI Chairman William G. McGowan announced yesterday.

A 6 percent increase for calls made between 5 p.m. and 8 a.m. will be imposed Aug. 1. And beginning July 1, MCI will raise rates by 5 percent for business customers who have private-line service.

Overall, McGowan says the changes will increase revenues by 3 percent, or $15 million, annually.

"The increase is needed to cover the higher costs" of being connected to American Telephone & Telegraph Co.'s local network, McGowan said. A 50 percent increase in these hook-up costs was mandated by the Federal Communications Commission last month.

Even so, McGowan said that overall long-distance rates for MCI customers should decline as a result of an expansion of service the District-based company is about to undertake to allow its customers to call anywhere in the United States.

MCI customers now can use the network only to call cities in which MCI operates--which accounts for about 70 percent of the nation's geographic area.

However, MCI plans to change all that by leasing WATS telephone lines--which allow customers to make a large amount of long-distance calls at large discounts--from AT&T to cover areas not now served by MCI.

As a result, McGowan says MCI customers will be able to make all their long-distance calls through MCI, no matter what the destination--still at a discount, because WATS rates will be lower than the ordinary rates most residential users have to pay.