There is no binomial name for a mosquito. Mosquitoes are members of the insect Order Diptera, which contains flies. Mosquitoes are also membersof the family Culicidae. Binomials are reserved for species names, and as such, each mosquito species would have its own unique binomial. The complete mosquito species name would also include the author of the species name. Hence a mosquito binomial might be Culex pipiens Linnaeus would be the complete name for a species of the genus Culex.
Another Answer There are 3100 species of mosquito Order Diptera Some genera are Culex AnophelesToxorhynchites