A number of circumstances could render a person ceremonially unclean and thus unfit for attending a sacred festival (see Leviticus 7:2–21). Often, an unclean person was required to be excluded from such functions only until the evening of the same day (Leviticus 15). This explains why Saul became suspicious after David did not arrive the next day.
Saul referred to David as the son of Jesse (also in 1 Samuel 20:31; 22:7), a description that functioned as David’s last name.