The ferry, which until now has only been known as Hull 802, will be called Glen Rosa.
CMAL, the body which owns CalMac vessels as well as the port and harbour infrastructure, announced the name after a public vote in which nearly 5,000 people took part.
Glen Rosa, which is Gleann Ruasaidh in Gaelic, was the most popular option, winning 52% of all votes cast.
The new vessel is the sister ship to the Glen Sannox, also being built at Ferguson Marine on the Clyde.
The ferries, which will serve islands off Scotland’s west coast, were due to be in service in 2018 at a price of £97 million, but delays have led to spiralling costs which could amount to more than three times that figure.
The name of the second vessel was announced after it emerged last week that sea trials for the Glen Sannox have been held up due to last-minute changes.
The Glen Rosa is currently due for launch in March 2024, and when completed both ferries will play a vital role in providing sailings to Arran.
CMAL chief executive Kevin Hobbs said: “The public’s response to the naming of Hull 802 has been fantastic to see and I’d like to thank everyone for taking the time to vote.
“Though we are disappointed in the delay to launching the vessel reported by Fergusons last week, we understand that the priority is ensuring that the newly named MV Glen Rosa achieves Maritime and Coastguard approval.
“We continue to work closely with the team at Ferguson Marine and can see great progress being made towards the delivery of both MV Glen Sannox and MV Glen Rosa.”
Robbie Drummond, chief executive of state-owned CalMac, said: “We are very much looking forward to MV Glen Rosa and MV Glen Sannox joining our fleet.
“These vessels will provide much-needed resilience to the Arran community, and to the network as a whole.”