From the experts:
Webster is one of several W-starting surname names back on the drawing board, now that it has recovered from its childlike eighties sitcom identity.
Webster was used in respectable numbers in the past--it reached a high of Number 388 in 1890--but like several other surnames starting with W, fell off the list completely in the 1940s. With its engaging nickname Webb, we can see it making a comeback.
Webster Young was a jazz trumpeter who played with most of the greats, but more prominent bearers wore Webster as a surname--in particular statesman Daniel and lexicographer Noah.