Dake
Likely a short English surname, possibly a variant of Day or Dake/Dack-style nickname forms, with the exact origin uncertain.
The #9,872 most common surname in the United States (2010 Census) — about 1 in every 94,216 Americans shares it.
Etymology
The historical dictionaries you provided do not give a secure standalone derivation for Dake, but they treat it as a surname form related to other short names such as Day and Dack. That points to a likely English nickname or shortened-name origin rather than a clearly occupational or locational one. Because the evidence is indirect, the literal root is best left uncertain.
History
The name appears in American records by the 19th century, and the excerpts show it being used as an established surname in the United States. One source also notes Virginia Dake in an early-American context, which suggests the name had already been present in North America by that time. Later surname-reference works group Dake with other brief surname forms, but they do not settle its exact derivation.
Origin
Regions
Variant spellings
Fun fact
The name is rare but long established enough to appear in old surname lists alongside many much more common English family names.
From the historical record
“* John de Dyneley holds the tonrth part of one Knight^s fee in Downum fDown- ham) of the said Dake,* Knights* Fees, 23 Edw. HI : Baines* Lane. ii. 694. 1803. Married — Thomas Liley and Charlotte Dineley : St. Geo. Han. Sq. ii. 274.”
— A Dictionary of English and Welsh Surnames (alternate scan)