Does agreeing with another company to rent cars at a certain price, then renting them to the customer at a higher price and taking the difference without the knowledge of the management, fall under the category of "selling what one does not own" if the management becomes aware of it?

What you do regarding brokering the rental of company cars falls into two categories: The first is when it is outside working hours, which is permissible for you. The second is when it is during working hours without the company's permission, which is not permissible.

As for your agreement with the customer on an amount greater than the company's price, if it is with the company's permission, then either you are an agent for the company and the increase goes to the company, and you receive an agency fee, or you are a broker, and you must inform the customer that the increase is your brokerage fee. However, if it is without the company's permission, you are not entitled to any of the fee; rather, it belongs to the company.

Your action does not fall under "selling what one does not own" because it is brokerage, not selling.