Is it permissible to take a 15% commission from a person nominated for a job, without the knowledge of the first party (the employer) regarding the details of the financial agreement between the nominator and the nominee?

What you intend to do by mediating between two people is called brokerage (simsarah), which is a permissible contract falling under the category of ju'alah (commission/reward). The majority of scholars hold that ju'alah is not valid as a percentage; rather, it must be a specified amount. If the amount paid for the service is known, the contract is permissible. However, if the amount is unknown, the majority of scholars consider the contract void, and thus it is preferable to avoid it. There is no harm in the first party not knowing what transpired between you and the second party, unless you are a private employee of the first party, in which case it is not permissible to take a fee from the second party without the first party's consent.