Ridiculous! (Ridiculous Lovers Book 1) by D. L. Carter

Identity theft regency style. After the death of her miserly cousin Antony North, Millicent Boarder is determined her family should never be poor or vulnerable again. To protect them she conceals her cousin's death and assumes his identity. Now she must face the Ton and the world as Mr. North and accept the price she must pay for her family's safety -- she will never be loved. Which means now is the perfect time for her to meet a duke!