ANSWER:

This is not from the sunnah.

The prophet’s uncle Hamzah and his beloved wife Khadeejah and many others died in his lifetime and he had never slaughtered a sacrifice specially for them. 

If you want, you can slaughter your own sacrifice and include in it all the deceased you want. 

QUESTION: Can I do a slaughter (of eid al adha) on the name of the deceased head of family, so that the slaughter will count for the whole family?