If you buy in your wife's name who doesn't file return of income or has no income source then you surely will receive notice asking for source of such investment but you can explain it.
However in that case the renting income and all will be clubbed in your income so it's better to not complicate transaction and take it in your name instead.
While showing such rent income you'll get a 30% standard deduction as well as deduction of 100% home loan interest from such renting income.
If you need detailed consultation you can have a phone consultation with me.
Hope you find the information helpful if you do please rate it 5 and provide your valuable feedback for my improvement.
Thank you