Everyone gets told that the name of Queens' College is spelt with the apostrophe after the final "s" because the College was founded by two Queens of England - first in 1448 by Margaret of Anjou (daughter of René of Anjou), wife of King Henry VI of England (the founder of King's College Cambridge), and secondly in 1465 by Elizabeth Woodville, wife of King Edward IV of England.
The use of the apostrophe in English to indicate the possessive is of no great antiquity. The earliest examples of the name of the College spelt with an apostrophe always have the apostrophe before the "s". The first example of the name of the College spelt with an apostrophe after the "s" was in 1823, in a printed and bound version of the form of service for the Commemoration of Benefactors, probably edited by G.C. Gorham.
The spelling changed from Queen's to Queens' in the calendar of 1831.
In Le Keux's Memorials of Cambridge, the author, writing about 1840, spells the name of the college as Queen's College, and appends a footnote:
“A custom has arisen latterly of writing the name Queens' College, as being the foundation of two queens. This appears to us an unnecessary refinement. We have the authority of Erasmus against it, who always calls his college "Collegium Reginae".
"Reginae" is Latin for "of the Queen", in the singular.
Despite this complaint, the change of spelling to Queens' became well established in the 19th century.
The formal corporate title of the College is now:
which shows both forms of spelling. This is formally correct. The name of the college when qualified by the patron saints is spelt in the singular; the short-form name is spelt in the plural.
Related spelling issues
Queens' Lane is named after the College, and should therefore be spelt in the same way.
Queens' Green is named after the College, and should therefore be spelt in the same way. Queens' Green is registered Common Land, owned by the Cambridge City Council, and, apart from its name, has nothing to do with Queens' College.
Queen's Road is named after Queen Victoria, so is correctly spelt Queen's.