I'm author of a Python package released under BSD license. This work was published in a GitHub repository. Someone forked my repository. Did some improvements and published code under MIT license with his name as author (removing mine as author). Is this allowed?
No, the other person was not allowed to remove the BSD license from your code. All forms of the BSD license say "Redistributions [...] must retain the above copyright notice, this list of conditions and the following disclaimer." If the downstream author has failed to include these components, then they are in violation of your license grant.
Yes, the other person is allowed to licence their own improvements under the MIT X11 license (or really any license, since code under 3- and 2-clause BSD licenses may happily stand alongside other code that is under virtually any license). However, they must obey the conditions in the BSD license grant on your original code, per the previous paragraph. In practice, I'm not really sure why the downstream author didn't just keep their changes under BSD as well, since it is more or less identical in effect to MIT X11.
As for the question of removing your name as author of the project: the license requires that downstream use of your code preserve your copyright notice, which includes your name. However, the BSD license does not impose further requirements about attributing you as the author (unless you've chosen the long-disused 4-clause BSD license). How prominent the downstream author should advertise your status as (co)author is purely a question of good manners, not legality. If you need to contact the author to rectify any missing copyright notice and BSD license terms, you might also kindly ask for a mention in the project README (or CONTRIBUTORS file, or other documentation) at the same time.