I've heard that MIT takes away most copyright
This is absolutely not correct; the MIT License (and all other open source licenses) rely on copyright law to be effective.
and permits free use
The MIT License permits use only within the conditions specified in the license. While that means you can do it without spending money, it is inaccurate to describe it as "free" (particularly within the open source community where "free" is an overloaded term).
Coming back to the point in hand:
I have a MIT licensed repository which is entirely copied just replacing the author name
The question here is exactly what did they do? The requirement in the MIT License is not very long ("The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software."). Therefore:
- If they replaced your name specifically in the copyright notice, then they are in violation of the license and you would be able to submit a claim against them.
- If they replaced your name anywhere else (e.g. there was a bit of text in the program which says "This software was written by the great programmer user18915229" and they changed it to "This software was written by the great programmer SomeOtherPerson"), that is absolutely fine - at least legally. Ethically it's questionable, but that's out of scope here.