The former Frederick Koch, who legally changed his name to Coke-Is- It, has negotiated an agreement with the Coca-Cola Company allowing him to keep his new name, a lawyer said today.

The agreement prohibits Mr. Coke- Is-It, 54 years old, from using the name commercially.

Mr. Coke-Is-It, father of the Olympic skier Bill Koch, changed his name in Windham County Superior Court in November because he was irritated by people who mispronounced his name as ''Kotch.'' But Coca-Cola objected to the use of its trademark.

The two sides reached a settlement that is expected to be filed in court later this week. It prohibits the lawyers involved from disclosing its contents.

''I can say that his name is still Coke-Is-It, and he will be able to use it,'' said John Burgess, who represents Mr. Coke-Is-It. ''You could speculate that the agreement prohibits any commercial use of the name.'' Mr. Burgess said the agreement did not involve a financial settlement.