Province 2 will decide about the name and capital through voting on Tuesday.
While the parties agree to keep Janakpur as the capital, they differ on the name.
Name and capital of the province can be decided only with two-third majority.
Rastriya Janata Party Nepal (RJP) has issued whip on its provincial assembly members to vote for Madhes as the name and Janakpur the capital.
CPN has demanded that the name be chosen Janaki while agreeing to keep Janakpur as the capital.
Nepali Congress (NC), meanwhile, has demanded it be named Mithila Bhojpura and Janakpur picked as capital.
Socialist Party Nepal has 30 lawmakers, RJP 25, CPN 32, NC 19 and Federal Socialist Nepal one in the provincial assembly.