Among the incarnations of Lord Vishnu, many are not aware of the fact that Vaamana and Parashurama do not appear to be married.
So are Matsya and Koorma.
In the case of Koorma, it may be taken as that since Lakshmi came out of the churning of the Ocean, the incident of Samudra Manthan and the marriage of Lakshmi with Vishnu subsequently, it may be concluded that Koorma Avatar had Lakshmi as his consort.
In Varaha Avatar Vishnu has Lakshmi on His Horns.
Narasimha has Lakshmi on His left Lap.
Rama has Sita: Krishna, Radha , Sathabhama, Rukmini:
Balarama. , Revathi.
Matsya being the first probably did not have a consort.
Given the fact, reiterated in all the Puranas that Lakshmi always accompanies Vishnu in His avatars, Parashurama and Vamana should have had Lakshmi as Consort.
Parashurama is the only Avatar of Vishnu that is present in both Avatars of Vishnu, in Rama and Krishna.
This could be because of the fact Parashurama is classified as Immortal, Chiranjivi.
Reference to Parashurama having been married is hard to come by.
So is about Vamana.
However there is a reference in Vishnu Purana that Parashurama was married to Dharani, an Avatar of Vishnu.
‘Parashurama, the destroyer of the warrior class, she was his wife Dharani; – from Vishnu Purana.
Reference and Citation.
I am deliberately quoting Brittanica as the source, though it quotes Vishnu Purana, A Hindu text, as we, Indians have a penchant for trusting western sources than Indian texts, even if these western sources rely on Indian texts!