My wife and I are recently married. We plan on filing jointly, but my wife has yet to change her name with social security. Does she need to do this before we can file?

No, but she need to file with the name currently on file with the SSA.

No, remember there is no legal requirement to even change your name many couples now don't even change the women's name any longer.

Agreed, there is no legal requirement to change the name.

But the name on the tax return MUST MATCH the name on the SSA records for her SSN, or the tax return will be rejected.