A bottle of Deanston 12-year-old malt was broken over the bow of the 90-metre Offshore Patrol Vessel in a ceremony at BAE Systems' Scotstoun yard.
The ship is expected to go into service next year and will be used for counter-terrorism, anti-smuggling and defence.
The MoD said work on HMS Forth and her sister ships was sustaining 800 Scottish jobs.
The vessels will be equipped with a 30mm cannon, a flight deck capable of accommodating a Merlin helicopter, and will be manned by a crew of 58 sailors.
It is the first of a fleet of new Batch 2 River-class OPVs being built on the Clyde, which are all expected to be in service by 2021.
Their construction has filled a gap in the order books of the Govan yard, where work is due to begin on eight Type 26 frigates this summer.
The Type 26 frigate, which is principally designed for anti-submarine warfare, will partially replace the current Type 23 frigate.
Each ship will carry a crew of 118, have a top speed of more than 26 knots and a range of 7,000 nautical miles. The first vessel is due to enter service in the early 2020s.
Defence Secretary Michael Fallon said that the work would safeguard hundreds of skilled jobs until 2035.
HMS Forth, the fifth Royal Navy vessel to bear the name over the past two centuries, is affiliated with the city of Stirling.
The MoD said the name maintained a connection that began when the people of the city adopted a previous ship with the name Forth during World War Two.
Minister for Defence Procurement, Harriett Baldwin, said the programme to build the ship was a vitally important part of the government's 10-year, Â£178bn plan to supply the Armed Forces.
She added: "From counter-narcotics operations in the Caribbean, to securing the UK's borders on patrols closer to home, the Royal Navy's new Offshore Patrol Vessels will help protect our interests around the world."
The first of a fleet of five warships being built on the Clyde has been formally named HMS Forth.