Nepali Congress (NC) has proposed to name Province 2 Mithila-Bhojpura and make Janakpurdham the capital.
NC lawmakers Shiva Chandra Chaudhary and Upendra Prasad Kushwaha have registered separate proposals for the name and capital respectively on Thursday.
NC had proposed the same name and capital when the provincial assembly last held voting on the topics.
Ruling Janata Samajwadi Party (JSP) and CPN (Maoist Center) earlier have separately proposed to name the province Madhes while CPN-UML has proposed to name it Janaki.
All four parties have proposed Janakpurdham as the capital. All the parties had proposed Janakpurdham as the capital even on the last occasion but the proposal could not get two-third majority for endorsement.
JSP has 56 lawmakers in the 107-strong provincial assembly where Maoist Center has expelled four of its lawmakers. UML has 21 seats, NC 19 and Maoist Center seven now.
The name and capital of the province have to be endorsed separately by two-third majority which no single party currently commands.
The provincial assembly secretariat had invited the parties to register their proposals for the name and capital by three Thursday afternoon.