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."

Swiss-born Mira Andres, of Aberystwyth, will get Â£1,000 and exhibit at Swansea's Elysium Gallery after winning the ESPY International Award 2015.
The University of South Wales graduate was recognised for her composition, The Black Crows of Borth.
It was inspired by the women who once walked the coastal path to Aberystwyth to sell herring and cockles.
Ms Andres, 28, who works as a freelance photographer and designer, said: "I'm very honoured and pleased to have won and I'm looking forward to exhibiting more of this work."
She was chosen as winner by judges Helen Sear and Peter Finnemore, two leading Welsh artists who have represented Wales at the Venice Biennale exhibition.

The 3,000m (10,000ft) volcano is in Argentina's south-western Neuquen province, near the Chilean border. It began spewing ash and gas on Saturday morning.
In Argentina, the authorities have told residents of local villages to monitor the situation.
Many people have already left the area as a precaution.
Ash has been raining down on both sides of the border.
The Chilean authorities raised the alert - first issued on Saturday - to the highest level in Biobio region after the Copahue volcano increased seismic activity overnight.
Roads were being cleared for possible evacuation.
The plume of smoke is about 1,500m (5,000ft) high and the wind is pushing it away from Argentina, said Chile's emergency office (Onemi).
Planes flying over the southern Andes have also been warned to avoid the area.
Hundreds of flights were cancelled last year due to the eruption of Puyehue volcano, in Chile.
That eruption caused huge economic damage not only to property in the area but also to tourism in Bariloche and other resorts.
The Copahue eruption comes at the height of the tourism season.
Visitors from all over the world go to the area in the summer months to enjoy the mountains, lakes and also the Copahue and Caviahue thermal spas.
Copahue in the indigenous Mapuche language means "sulphur waters".
The first of a fleet of five warships being built on the Clyde has been formally named HMS Forth.
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A Ceredigion photographer has won an international competition with a series of pictures taken in Borth.
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Chile has raised the alert level for the Copahue volcano to red, the highest possible.