Yes, there is a connection between the Avon Lady and Shakespeare’s hometown Stratford-upon-Avon.
In 1896 in New York City, D. H. McConnell abandoned door-to-door book selling and formed the California Perfume Company, which marketed scents the same way.
His company expanded and McConnell built a factory in Suffern, New York.
On the 50th anniversary of the company, McConnell changed its name. He chose Avon because he admired Shakespeare.