Its a nickname. From a wartime song.
"Cpl. Bert Gold and Lt. Ken Hart, both of Long Beach, New York, co-wrote "Dogface Soldier" in 1942. They wrote the song about common soldiers but it came to the attention of then Third Infantry Division Commander Maj. Gen. Lucian K. Truscott who had "Dogface Soldier" adopted as the division's song. The song was immensely popular. Soldiers sang it, marched to it and danced to it.
It made a public debut in the 1955 Audie Murphy film "To Hell and Back". Over 300,000 copies of the recording were sold. "Dogface Soldier" is the most publicized and well known song of World War II.
"Dogface Soldier"
I Wouldn't Give A Bean / To Be A Fancy Pants Marine, / I'd rather Be A Dogface Soldier Like I Am. / I Wouldn't Trade My Old O.D.'s / For All The Navy's Dungarees / For I'm The Walking Pride Of Uncle Sam; / On All The Posters That I Read / It Says The Army Builds Men / So They're Tearing Me Down To Build Me Over Again / I'm Just A Dogface Soldier / With A Rifle On My Shoulder / And I Eat A Kraut For Breakfast Everyday. / So Feed Me Ammunition, / Keep Me In The Third Division, / Your Dogfaced Soldier Boy's Okay"
The figures are loosely based on comic characters.
(not quite sure about the quote above claiming its the most well-known song of WWII though,

)