I had a full legal name change and updated it with the IRS and everywhere else I am suppose to. Do I need to submit the court order to turbotax?

No, there is nothing that you need to submit to TurboTax with regard to your name change.

When you are working on your tax return, just enter your new name in the appropriate fields.  As long as your social security number and new name matches in the taxpayer database at the Social Security Administration when your return is filed, there should be no problems. 

No, nothing to TurboTax.  On your tax return you use the name that is on your current Social Security card.

To change any information on your TurboTax account -

1. Sign in to your account.
2. Select Intuit Account on the left, and you'll see your Account Settings.
3. Select either Profile or Security depending on which options you want to update.
4. Select Edit next to the option(s) you want to change.