Persian blue (not to be confused with prussian blue) comes in three shades: Persian blue proper—a bright medium blue; medium Persian blue (a medium slightly grayish blue that is slightly indigoish); and a kind of dark blue that is much closer to indigo; this darker shade of Persian blue is referred to as Persian indigo or dark Persian blue.).
The color Persian blue is named from the blue color of some Persian pottery and the color of tiles used in and on mosques and palaces in Iran and in other places in the Middle East. Persian blue is a representation of the color of the mineral lapis lazuli which comes from Persia and Afghanistan. (The color azure is also named after the mineral lapis lazuli.)
The first recorded use of Persian blue as a color name in English was in 1669.
The source of this color is a color sample taken directly from the Persian blue tiles shown in the photograph displayed in the Wikipedia article on the Shah Mosque of the interior tile work of its dome.
The first recorded use of regimental (the original name for the color now called Persian indigo) as a color name in English was in 1912.
The source of this color is the ISCC-NBS Dictionary of Color Names (1955), a color dictionary used by stamp collectors to identify the colors of stamps, now on the Internet--see sample of the color Persian blue (color sample #178) displayed on indicated web page: