Although we might see a change in color due to the coincidence of partial lunar eclipse that's also happening tonight; probably we'll see the moon a bit orange-y, but who knows it might actually turn somewhat pink tonight haha! The lunar eclipse is visible in Asia, Africa and Europe.
According to various sources, the term Pink Moon dates back to the ancient times where moons were named after the different seasons important to ancient tribes, describing the prominent scenario seen on earth:
Full Pink Moon (April): Bloom of herb moss pink or wild ground phlox during spring.
Full Flower Moon (May): When flowers are abundant
Full Buck Moon (July): New antlers of buck deer grow out of their foreheads.
Full Sturgeon Moon (August): Sturgeon is a large fish. During this month, sturgeons were caught without difficulty, probably it's the time when the eggs hatch and mature.
Full Harvest Moon (September): Also called the Full Corn Moon. A time of harvest. I remember the game Harvest Moon, they probably get it from this term.
Full Hunter's Moon (October): Native Americans hunt in preparation for the winter.
Full Beaver Moon (November): Either they hunt for beavers for their fur or beavers starts to prepare for winter.
Full Cold Moon or Full Long Nights Moon (December): Time of winter where the nights are coldest, longest, and darkest.
Source 1, Source 2, Source 3, and thanks swashbuckler for the photo