With #[cfg(not(any(Py_LIMITED_API, PyPy)))], Borrowed<'a, '_, PyType>::name implementation delegates to tp_name.
However, tp_name is not consistent.
For pure Python types Borrowed<'a, '_, PyType>::name returns different result if compiled with or without abi3 feature.
Solution
Make Borrowed<'a, '_, PyType>::name follow __name__ behavior, and expose Borrowed<'a, '_, PyType>::module.
I will open a PR.