The Orthodox Presbyterian Church was originally named the Presbyterian church of America. The Presbyterian Church in the U.S.A. brought a law suit against the new denomination claiming the similar name would cause confusion. You can read about the suit in Chapter 12 of The Presbyterian Conflict by Edwin Rian.
Thomas R. Birch, reporting on the Fifth General Assembly of the Presbyterian Church of America in the Presbyterian Guardian, wrote about the following about debate over the choice of a new name.
The Rev. Edwin H. Rian then reported for the Home Missions Committee on the progress and status of the suit. The committee recommended a discontinuance of the appeal. The motion to adopt this recommendation was laid on the table pending a consideration of the choice of a new name for the denomination. Suggestions for the name were freely made from the floor of the assembly and names were added to this list from correspondence received from those unable to attend the assembly. Six ballots were necessary before the final choice of the name, “The Orthodox Presbyterian Church,” was made.
In the course of the debate about ten names were suggested, some of which did not receive even one vote. Each name that was seriously considered was fully discussed by those who favored it and those who disliked it. There was no slightest tendency to limit debate or to hurry the assembly into the adoption of any name whatever. It was obvious early in the discussion that most of the commissioners preferred one or another of the following four names: The Orthodox Presbyterian Church; The Protestant Presbyterian Church of America; The Presbyterian and Reformed Church; and The Evangelical Presbyterian Church.
Chief protagonist for “The Orthodox Presbyterian Church” was the Rev. Everett C. De Velde of Cincinnati, Ohio, and he was ably assisted by many of his colleagues. Several members of the faculty of Westminster Seminary preferred “The Presbyterian and Reformed Church,” but it did not receive widespread support due to the belief on the part of many that it would cause confusion and misunderstanding, and would sound like a merger of two other churches. “The Evangelical Presbyterian Church” lost ground rapidly in the balloting because of the contention that the word, “Evangelical,” had ceased to have its original meaning and would not present a clear picture of the church’s position. “The Protestant Presbyterian Church of America” was warmly championed throughout the almost eight hours of debate and was not eliminated until the final ballot. It was understood by its defenders as signifying the “protesting” church and was frequently pronounced with the accent upon the second syllable. Those opposed to it pointed out that it would not be thus pronounced by the general public, to whom it would simply mean “non-Catholic.”
“The Orthodox Presbyterian Church,” the name finally chosen on the sixth ballot, had a host of virtues which were fully pointed out by its supporters. It told the world exactly where its members stood in the controversy between Christianity and Modernism, it declared that they took their confession of faith seriously, and it drew a precise theological distinction that was hardly capable of misunderstanding. As one member described it, “It has teeth.”
It is the option of your reporter that no one who had the privilege of listening to the lengthy and free debate left the assembly with a feeling of dissatisfaction or discontent over the final decision. Even those who had favored some other name seemed quite ready to fight in the future under the banner of “The Orthodox Presbyterian Church.” It has seldom been our privilege to hear a more orderly, deliberative, exhaustive, or friendly debate on any subject whatever. The final ballot was not taken until about 11 o’clock in the evening, yet there was no impatience or tendency to hurry a decision. The importance of the occasion seemed recognized by everyone, yet tension and bitterness were completely missing. After the final selection of the name, the following resolution was adopted: “Resolved that this Assembly declares the name of this Church changed from The Presbyterian Church of America to ‘The Orthodox Presbyterian Church,’ effective March 15, 1939.” The assembly then directed its counsel to discontinue the appeal before the Supreme Court of Pennsylvania, also effective March 15, 1939.