If you have trouble filing with your new married name you can still use your maiden name on the tax return. The new SS card might be too late for the IRS to double check with your return. I would try using your maiden name. Your work and banks shouldn't be a problem.
You should usually file a Joint return which is only 1 return combined for the both of you. Joint has the lowest tax rates and the highest Standard Deduction. And if you are in a Community Property state MFS gets tricky to figure out. Make sure to stick with this one account for the future. Just ignore the other spouse's account.
Start a return and enter your name and info. It will ask if you are single or married. When you pick married a box will open for her name and info. Then when you enter any forms like W2s or 1099s be sure to pick who it is for. That is very important. When you get married you are considered married for the whole year even if you got married on Dec 31.
Getting Married FAQ
https://ttlc.intuit.com/community/tax-filing-status/help/what-does-getting-married-mean-for-my-taxes...
Tax info on getting married
https://turbotax.intuit.com/tax-tips/marriage/getting-married/L0DvEUlEC
Did you both use Turbo Tax last year?
You can not transfer from or combine 2 returns or accounts. Just pick the return for the spouse that has the most complicated return to enter or has any depreciation or business or more investments. Or use the account/return for whoever you want to be listed first going forward (by the way you can not change the order of the names). Then add the other spouse's name, ssn and info to it.
But if you want to keep the prior accounts separate from the new Joint account then start a new account. Online is only good for one return per account. But you can use the same email address for 5 accounts.
How to start a new online return
https://ttlc.intuit.com/community/using-turbotax/help/how-do-i-start-another-return-in-turbotax-onli...
