payment of rent to lessor

Dear Sir,
I own a commercial complex which was build on my partnership firm name where me and my wife is the partner. The land on which the commercial complex is there also is on my name. Now I have leased out the complex to a third party vide one unregistered lease dead where both me and my firm both are party to the lessee. So far they were paying rent on my firm's name and I want them to pay the monthly rent in my firm's name only. But now they want us to do the lease agreement registered.
My problem here is I can not get the lease done on my firm's name with this third party as both building permission and land permission is in my name.
So my question here is can i modify the lease deed where in the lessor is me and lessee is the other party and i include a clause that " I would like the lessee to pay the rent to my firms name only and I wont have any objection to it in near future. "
Is it possible to executive the lease deed that way ?

Regards

Prashant