The missing name (once more torn away) would be a short name

—shorter, it would appear, than, say, the name "Betsy." It might possibly be "Mama"--as Louisa seems apt to feel "quite alone" when she is away (see S23, S25, and J1). And Louisa's labours in the kitchen may have been undertaken to allow her mother to leave for Mrs. Prescott's right after dinner. If it is Mama that accompanies Phebe, then tea must have been prepared by the fourth oldest daughter, Mary Ann--or Papa--unless Charlotte, or Mama herself, returned in time.