All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is permissible for a woman whose husband died to inform the people that she is the widow of so and so who is dead because she is telling true information about what happened.
However, it is not permissible for a woman to be traced back to the family of her husband neither when he was alive nor after his death. Rather, a woman is obliged to be traced back to her father as Allaah Says (what means): {Call them (adopted sons) by (the names of) their fathers, that is more just with Allaah.}[Quran 33:5] Indeed, we clarified this in Fataawa 118807 and 89932.
As regards supplicating for her husband after his death, then this is permissible; rather, this is desirable and this is being faithful to him. How can a wife be prevented from a good supplication to her husband who is most in need for this? It is even permissible for her to supplicate for all the deceased Muslim people and to the people who are still alive as well, as there are no religious texts that prevent a woman from supplicating to someone who is a non-Mahram to her.
Furthermore, it is permissible for you, dear sister, to gift the reward of reciting the Quran and other acts of righteousness to your husband. This is something that will benefit him, Allaah willing, as clarified in Fatwa 84122.
Allaah Knows best.