I suppose this question points to a particular source, which I have not found yet.
Right on the contrary, many sources I found stated that the uniforms worn in the Civil War varied a great deal, so it is hard to say which coat the submitter had in mind when asking that question.
From Wikipedia:
The Uniform of the Union Army was widely varied and, due to limitations on supply of wool and other materials, based on availability and cost of materials during the United States Civil War.
However I have found the "Revised Regulations for the Army of the United States" dated 1861, which has a section about overcoats. The name for overcoats, worn in winter, is stated as
"Cloak coat" - so that might be the official answer. Although many sources also refer to the name as
"Greatcoat".
https://www.regtqm.com/Great-Coat-Infantry-Pattern-p/feu-002.htm
As to shoulder flaps, in this official regulation there is no information about the purpose of such a flap or the number of flaps designed for infantry coats.
OVERCOAT
For Commissioned Officers.
1559. A
"cloak coat" of dark blue cloth, closing by means of four frog buttons of black silk and loops of black silk cord down the breast, and at the throat by a long loop
á échelle, without tassel or plate, on the left side, and a black silk frog button on the right; cord for the loops fifteen-hundredths of an inch in diameter; back, a single piece, slit up from the bottom, from fifteen to seventeen inches, according to the height of the wearer, and closing at will, by buttons, and button-holes cut in a concealed flap; collar of the same material as the coat, rounded at the edges, and to stand or fall; when standing, to be about five inches high; sleeves loose, of a single piece, and round at the bottom, without cuff or slit; lining, woolen around the front and lower border, the edges of the pockets, the edges of the sleeves, collar, and slit in the back, a flat braid of black silk one-half inch wide; and around each frog button on the breast, a knot two and one-quarter inches in diameter of black silk cord, seven-hundredths of an inch in diameter, arranges according to drawing; cape of the same color and material as the coat, removable at the pleasure of the wearer, and reaching to the cuff of he coat-sleeve when the arm is extended; coat to extend down the leg from six to eight inches below the knee, according to height. To
indicate rank, there will be on both sleeves, near the lower edge,
a knot of black silk braid not exceeding one-eighth of an inch in width, arranged according to drawing, and composed as follows:
1560.
For a General--of five braids, double knot.
1561.
For a Colonel--of five braids, single knot.
1562.
For a Lieutenant-Colonel--of four braids, single knot.
1563.
For a Major--if three braids, single knot.
1564.
For a Captain--of two braids, single knot.
1565.
For a First Lieutenant--of one braid, single knot.
1566.
For a Second Lieutenant and Brevet Second Lieutenant--a plain sleeve, without knot or ornament.
For Enlisted Men.
1567. Of all Mounted Corps--of sky-blue cloth; stand-and-fall collar; double-breasted; cape to reach down to the cuff of the coat when the arm is extended, and to button all the way up; buttons (1467).
1568. All other Enlisted Men--of sky-blue cloth; stand-up collar; single-breasted; cape to reach down to the elbows when the arm is extended, and to button all the way up; buttons (1467).
1569. For Cavalry--a gutta-percha talma, or cloak extending to the knee, with long sleeves.
http://howardlanham.tripod.com/unireg.htm
As for the purpose of the shoulder flap, I found in various sources that a "shoulder flap" in military clothing is a so called "
gun flap", designed to protect the garment from being damaged when the wearer is shooting (or shouldering) his gun. It also offers a kind of padding against the effects of the recoil.
On the other hand, no illustration shows any gun flaps on a Union greatcoat, while many show a cape. The book
"Uniforms of the Civil War" describes an Infantry overcoat as follows:
https://books.google.de/books?id=I2...er flaps infantry greatcoat civil war&f=false
There is no mention of any shoulder flaps,
only a cape is mentioned.
The purpose of a cape is providing warmth and rain protection.
So here comes my final answer:
- Name of the coat: Cloak Coat
- Purpose of a "shoulder flap"(a) or cape (b): rain protection (b), warmth (b), protection of garment from effects of firing or carrying a gun (a), protection of the wearer from recoil (a)
- Number of shoulder flaps on Union Infantry greatcoats: (none) - one cape
That's the best I could come up with within a reasonable amount of time.