No, but they are in the line of succession to the Monegasque throne, except of Camille, because she is illegitimate
Current Monarch: Albert II
HRH The Princess of Hanover, Hereditary Princess of Monaco, elder sister of the Prince
Andrea Casiraghi, elder son of the Princess of Hanover and Stefano Casiraghi
Pierre Casiraghi, younger son of the Princess of Hanover and Stefano Casiraghi
Charlotte Casiraghi, daughter of the Princess of Hanover and Stefano Casiraghi
HRH Princess Alexandra of Hanover, daughter of the Prince and Princess of Hanover
HSH Princess Stéphanie of Monaco, younger sister of the Prince
Louis Ducruet, son of Princess Stéphanie and Daniel Ducruet
Pauline Ducruet, daughter of Princess Stéphanie and Daniel Ducruet
And I read that Andrea would be, if his mother succeeds, HSH Hereditary Prince Andrea of Monaco, Marquis of Baux and a Grimaldi. So no dynasty called Casiraghi (but it sounds nice) when Andrea is the sovereign Prince.