Yes, Becky is commonly used as a diminutive or nickname for Rebecca. Many names have shorter or more casual forms, and Becky is one of the affectionate variations for Rebecca.
Short form of Rebecca. A Hebrew name meaning: to bind (together).
Rebecca
Usually the nickname for Rebecca is 'Becky.'
Rebecca "Becky" Adlington
Rebecca McGill goes by Lola Storm, and Becky.
Rebecca "Becky" Adlington
Rebecca
Rebecca Tarbotton went by Becky.
Rebecca Blasband goes by Becky.
Rebecca Demmen goes by Becky.
Rebecca Etheridge goes by Becky.
Rebecca Domingo went by Becky.