Gorton
A habitational surname from places named Gorton, especially the district in Manchester, meaning a settlement on or near a muddy or goat-associated stream or enclosure, depending on the place-name root.
The #8,060 most common surname in the United States (2010 Census) — about 1 in every 75,121 Americans shares it.
Etymology
Gorton is a place-name surname, taken from a locality rather than from a personal characteristic or occupation. The historical dictionaries in your excerpts point to Gorton as a chapelry in Manchester and treat the surname as locational. The first element is usually explained from an Old English word such as gor, meaning dirt or mud, though place-name analyses can vary; the second element is the common Old English tun, meaning an enclosure, farm, or settlement.
History
The surname arose independently for people who came from Gorton, especially in Lancashire/Cheshire records. Because place-name surnames often spread with migration, it later appears beyond the original district and is now found more widely in England and overseas. The form is stable and straightforward, with the modern surname matching the place-name closely.
Origin
Regions
Variant spellings
Fun fact
One of your excerpted sources explicitly identifies Gorton as a chapelry in the parish of Manchester, showing how directly surname and place-name were linked in older reference works.
From the historical record
“Gorrinje. GORTON. A chai;)eh'y in the parish of Manchester. GOSDEN. See xmder Den. GOSHAWK. The bird. GOSLAND. See Goose. GOSLEE. See Goose. GOSLTN. See Gosling.”
— Patronymica Britannica: a dictionary of the family names of the United Kingdom