https://en.wikipedia.org/wiki/Washington_family

“The Washington family traces its roots to Sir William de Hertburn, who in 1183 traded his manor of Hertburn for that of Wessyington in northeast England near the border with Scotland. . .

Sir William, as customary, adopted the name of the estate "de Wessyington" later becoming the surname "Washington". . .

For the next 500 years or so the Washington family would continue to be distinguished members of the County Durham nobility and landed gentry.”

https://www.nationaltrust.org.uk/washington-old-hall/features/from-wessington-to-washington

“. . .the family adopted a new coat of arms which featured two bars (stripes) and three mullets (stars) in red against a white background. . .”

https://en.wikipedia.org/wiki/Coat_of_arms_of_the_Washington_family

Coat of arms of the Washington family was adopted in the 12th century, when the Washington family took possession of Washington Old Hall, County Durham, England.

Crest - From a crest coronet a raven rising wings elevated and addrosed proper.

Escutcheon - Argent two bars Gules, in chief three mullets of the second.

Motto - Exitus acta probat (The outcome is the test of the act)

https://upload.wikimedia.org/wikipedia/commons/thumb/5/59/Coat_of_Arms_of_George_Washington.svg/330px-Coat_of_Arms_of_George_Washington.svg.png

The design (three red stars over two horizontal red bars on a white field) has been used since 1938 as the flag of the District of Columbia. The shield of the Washington Coat of Arms appears in the design of the Purple Heart Medal.