If the social security number on the 1099-B is correct just enter it on your tax return as is. The IRS will track the tax ID number more than the name.
If the name is a person that you used to share the account with then you need to get their name off of it. Close the account and re-open it elsewhere if you have to.
If they just have your name misspelled then ask them to fix it going forward.
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