For your federal taxes, it won't be a problem. Where you may encouter an issue is your state taxes, but this depends on the state.
Since your Social Security card reflects your new name, be sure to file using this name. If it was a very recent change, and your return is rejected for a mismatch then change the name to match the old records and rebubmit.
If the federal is accepted under your new name, it is likely that your state will accept it also unless you are in one of the few states (such as Illinois and New York) where the license information is used to verify identity. If that is the case, any rejection mesage should offer the best remedy whether that is to make an adjustment and re-file or to print and mail the return instead.
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