No records show his name as Harrison Archibald or Archibald Harrison, but the marriage record has his name as Archibald, while nearly all other records give his name as Harrison. There can’t have been two Rameys of the same age in the area with wives named Mahala Jones, though. (See, e.g., the birth record of their daughter Emily, or the death record of their son Alfred.)

1850 census of Fleming Co., Ky, division 2, p. 362, lists as family #30:
Harrison Ramey, 35; Mahala, 35; Rachel, 15; Alvin, 13; Martha Jane, 11; Alfred, 9; Page (male), 9; Harrison, 4; John, 1. All born in Ky.

(The preceding family is that of Archibald Ramey age 90 with wife Mary Ann age 70, and the following family is that of Jeremiah Ramey age 36 with wife Eunice. This is in the part of Fleming Co. that became part of Rowan Co. when it was formed in 1856.)

1860 census of Rowan Co., Ky, enumerated 11 June, lists as on p. 1 as household #1:
Ramey, Harrison, 45, farmer; Mahala, 44; Rachael, 23; Martha, 20; Alfred, 19; Page (male), 16; Harrison, 14; John, 12; Emma, 5; Lucy, 3. All born in Ky.

1870 census of Rowan Co., Pearce precinct, p. 129A, lists as family #104:
Ramey, Harrison, 56, farmer; Maria, 43, married in Dec.; Emily, 17; Lucy, 12. All born in Kentucky.

1880 census of Rowan Co., Pearce precinct, enumerated 1 June, lists on p. 28 as family #241/243:
Ramey, Harrison, 65, farmer; Maria, 53, wife; Rachel, 40, dau; Lucy, 23, dau; Martha, 3, granddau. All born Ky/Ky/Ky.

Morgan Co. marriage books record the marriage on 26 Sep 1833 of Archibald Ramey and Mahala Jones, by Moses B. Evans.

Judging by birth records for Emily, Archibald is apparently the same person as Harrison Ramey.