Can I use the contraction after a proper noun? Please look at this sentence.
Anu'd been living with her parents and two elder brothers. [For Informal Context]
We can certainly use a contraction after a proper noun. "John's gone away", for example, is fine in informal use.
Have and had are a bit more problematic, I think. We would certainly elide "Anu had been living..." in speech, but it looks odd in writing unless you are consciously reproducing very informal speech in a story or play.