No those are the actual names for the denominations as set forth in sec 9 of the Mint act of 1792. and the Coinage act of 1849 for the Double Eagle
SEC. 9. And be it further enacted, That there shall be from time to time struck and coined at the said mint, coins of gold, silver, and copper, of the following denominations, values and descriptions, viz. Eagles—each to be of the value of ten dollars or units, and to contain two hundred fort-seven grains and four eighths of a grain of pure, or two hundred and seventy grains of standard gold. Half eagles—each to be of the value of five dollars, and to contain one hundred and twenty three grains and six eights of a grain of pure, or one hundred and thirty five grains of standard gold. Quarter Eagles—each to be of the value of two dollars and a half dollar, and to contain sixty one grains and seven eights of a grain of pure, or sixty seven grains and four eights of a grain of standard gold.
From the Act of 1849
Double eagles, each to be of the value of twenty dollars, or units