The names were approved by the Queen.
Both boats will be used to patrol HMNB Gibraltar and British Gibraltar Territorial Waters (BGTW).
A £9.9m six-year contract was signed with Merseyside-based Marine Specialised Technology (MST) last July to build the new Gibraltar Squadron Fast Patrol Craft.
The first boat is expected to be delivered later this year, with the second in the first few months of 2022.
The name 'Dagger' is new to the Navy, having originally been planned for a weapon-class anti-submarine escort in the Second World War, only to be cancelled as the conflict ended.
Just one previous HMS Cutlass served under the White Ensign in the 1970s.
It was used to train British and NATO warships to meet the threat of fast missile or torpedo craft.
The boats can travel at speeds of up to 40 knots and are propelled by a trio of Volvo D13-1000 engines which each provide 1,000 horsepower of thrust, as well as three MJP350X water jets.
Each vessel can fit six crew members and six passengers.
Initially, they will carry three purpose machine-guns and will be fitted for, not with, 0.5-calibre heavy machine guns.
The two new boats will replace the current Gibraltar Squadron Fast Patrol Craft, HMS Pursuer and HMS Dasher.
Cover image: Library photo of Gibraltar Squadron fast patrol boats (Picture: MOD).