My husband died in July 2021 and while filing 2021, should I now become first name for married filing jointly?

If his name was first on the prior year tax returns then for tax year 2021 his name should remain first on the federal tax return to avoid any confusion at the IRS.

So sorry for your loss.   No.   Do not change the order of your names.

 For the year that your spouse died, you can still file a joint return.  That way, you will get the married filing jointly standard deduction of $25,100 (+ $1350 for each spouse 65 or older) which will lower the amount of income you are taxed on.

In My Info, you will need to indicate that your spouse died. When his name is in My Info,  there is a screen early in the interview that asks "Do any of these apply to [name] ?’” where you will do that, and then a drop down will appear where you can enter the date he passed.

If you have dependent children still living at home, you will be able to file as a qualified widow for the next two years after this tax return.  Post back if you need further help.