Unable to correct husband name in Death Certificate.How to prove that I am widow in Govt. Jobs

Hii All, SITUATION ==> My husband died on 25 September 2020 due to illness (scrub typhus) in PGIMS,Rohtak (Govt. Hospital). I have an 5 year old daughter with me and there is no support from in-laws and very less support from my family We belong to (Village:Ranoli) Bawal district,Haryana In aadhar card and all other document my husband name is "DARYAV NEHRA" but in all medical reports during his treatment his name was written as "DARYAV SINGH". I accept its my stupdity that I should have got his name corrected then and there but due to so much of worry and unease at that moment, it didn't occured to me to look at his name in the medical reports. Now the death certificate is made with name as "DARYAV SINGH". I have made all efforts, visited hospital almost 30-40 times but they only respond that we JUST CAN'T CHANGE IT. There is no procedure to change name to DARYAV NEHRA in case the name in all govt. medical report name is DARIYAV SINGH. MY CONCERN ==> (1)Is there any way to get his name change in Death Certificate considering in all medical reports my husband name is incorrect. (2) How to prove that I am an widow in any upcoming government recruitment(I do have Marriage Certificate with correct name of my husband in it.). :