No your wife's name will not be added to the mortgage contract. Her income can be added to the household income to qualify for the modification but the mortgage will stay in your name only.
It does not matter who lives in the house and contributes to the household income or what the source of the income is. It could be your Grandmother on disability or Social Security. Her contribution to the household income can be counted in whole or in part but only the names that were originally on the mortgage contract are on the contract after the modification of the loan.
If only your name is on the mortgage and you add income from everyone who lives in your house to qualify for a mortgage loan modification, after the loan is modified the mortgage is still only in your name.
Different Income Rules For Loan Modification And Loan Qualifying
The income rules for loan modification are different than qualifying for a new mortgage loan. When you first take out a loan, all income earners who contributed to the income figures used to qualify for the loan would be put on the mortgage contract.
When you modify a loan you are only restructuring the terms of the loan, interest rate, length of the loan, the unpaid principal balance and of course the monthly payment. Modifying a loan does not require qualifying for a new loan.
If you wanted to add some one to the mortgage so their name would be on the mortgage you would basically be getting a new loan and would have to go through the qualifying process for that new loan.