Is it permissible, Islamically, to take a commission in exchange for supervising the rental of shops and managing their accounts, as offered by the employer?

It is not permissible to delegate the work entrusted to you or to take a commission on it without the employer's permission, because it was entrusted to you due to your specific trustworthiness, and you are a private employee for him. Furthermore, you receive a salary for this work, so you are not entitled to take a commission on it.