Hra

Explanation to sec 10(13A) provides as follows:

Explanation.—For the removal of doubts, it is hereby declared that nothing contained in this clause shall apply in a case where—

      (a)  the residential accommodation occupied by the assessee is owned by him ; or

      (b)  the assessee has not actually incurred expenditure on payment of rent (by whatever name called) in respect of the residential accommodation occupied by him ;]

           So if the above does not holds true then you cannot claim exemption on account of HRA.  You will be required to continue the lease arrangement between you & the co.  If you take your wife’s name then there would be problem for taxation point of view, because the taxation authorities would question the source of income of your wife for payment of the rent.