"[T]he pirated American edition of 1768 was the first to name Rasselas on its title page; but in fact the heading of the first page of text of every edition published in Johnson's lifetime reads: "The History of Rasselas, Prince of Abissinia". For convenience and recognizability Johnson's tale is referred to elsewhere in this encyclopedia as simply Rasselas (1759)."
--SFE3, biographical entry by John Clute and Peter Nicholls
--SFE3 lists these full titles from early title pages:
• The Prince of Abissinia: A Tale (1759)
• The History of Rasselas, Prince of Abissinia: An Asiatic Tale (1768)
• The History of Rasselas, Prince of Abissinia: A Tale (1787)
New edition
Edited with an introduction by D. J. Enright
For this ISBN as of 2019-07-29 Amazon UK shows:
• "[title deleted] (English Library) Paperback – 25 Nov 1976"
• "Penguin Classics; Reprint edition (25 Nov. 1976)"
and provides front cover image as Penguin Classics, with "Look inside" a book with matching cover:
Copyright page (quote three lines):
-- Published in Penguin Books 1976
-- Reprinted in Penguin Classics 1985
-- 15 17 19 20 18 16 (that is, 15th printing)
Thus the Penguin Classics is a later ed./printing.
Page numbers below are from the Contents list of that 15th printing, whose listings "Select Bibliography 36" and "Notes 151" suggest no change from the 1976 edition that the national libraries report (BL and LCCN, below).
British Library BL and Library of Congress LCCN provide matching data except:
• location "Harmondsworth" [UK] vs. "New York, [etc.]"
• BL reports paper cover and price £0.60
Both give size 19cm, which is ambiguous, but ISFDB records (5) show this is a pb-only series during the 20th century.