Kaye
Usually a spelling of Kay, a surname that most likely began as a nickname or as a place-based name near a quay or quay-side.
The #4,113 most common surname in the United States (2010 Census) — about 1 in every 35,788 Americans shares it.
Etymology
Kaye is generally treated as a spelling variant of Kay. In surname studies, Kay is often linked either to a nickname from the Middle English word for a key or to a locational name from a quay or quay-side, from Old French and Middle English forms meaning a wharf. The historical sources you provided also show Kaye being grouped with Kay rather than as a distinct surname with a separate secure origin.
History
Older writers sometimes tried to connect the name with Arthurian legend and a supposed ancient British lineage, but that is best treated as family tradition rather than reliable etymology. In actual records, the surname appears in several spellings, including Kay, Kaye, Ka, and K. The form Kaye has been especially common in England, particularly in northern records, and it remains best understood as a spelling variant rather than a separate origin.
Origin
Regions
Variant spellings
Fun fact
One 19th-century writer noted that the name could appear in records as K, Ka, Kay, or Kaye, showing how unstable spelling often was before modern standardization.
From the historical record
“pedition. KAYE. KAY. " The family of Kaye," says an old statement, " is of great antiquity in the county of York, being descended from Sir Kaye, an ancient Briton, and one of the KnigliU of the warliliS Table of that noUe Prince Arthur, floiver of cMvalrij ! .'" It is added that his descendant at the period of the…”
— Patronymica Britannica: a dictionary of the family names of the United Kingdom