Becky Sharp was credited with the strip 'Cynical Susie' in 1935, which was originally created by LaVerne Harding (1933-34) and also drawn by Bernard Dibble.
Cynical Susie strip, attributed to "Becky Sharp"
It's possible that was a pseudonym for one of those artists, as pointed out in an email by Stuart Cooper:
"The signature appears to be in quotation marks in the example you post, suggesting acknowledgement of a pseudonym. It should be kept in mind that "Becky Sharp" (an adaptation of Wm. Thackeray's novel "Vanity Fair") was the first full Technicolor feature film, released in 1935, just as "Cynical Susie" began to be credited to this name. It is my understanding that the film did very badly and was a notorious laughing-stock at the time.
Since the strip 'Cynical Susie' was set in Hollywood, it's very likely that "Becky Sharp" was one of the two credited artists (LaVerne Harding or Bernard Dibble) using that pseudonym for a while as a joke at the expense of the film. In fact, since LaVerne Harding started working for Walter Lantz as an animator around that time, I strongly suspect "Becky Sharp" was simply Harding moonlighting under that pseudonym, possibly due to union rules restricting her from outside work."