She was most likely named after her paternal aunt, Cecily Neville, Duchess of York.
She first married Henry de Beauchamp, 1st Duke of Warwick, and the only King of the Isle of Wight (as well as of Jersey and Guernsey).
Their only daughter was Lady Anne Beauchamp, who was allowed to succeed as suo jure 15th Countess of Warwick.
Upon the death of the 15th Countess, the title was inherited by her paternal aunt, also named Lady Anne.
Lady Anne married Cecily's brother, Richard Neville, who would become jure uxoris 16th Earl of Warwick.