Is it permissible to continue collecting the same rental value ($1000 per month) for the restaurant after the customers have become accustomed to the tenant's name and the equipment has worn out, knowing that the tenant is requesting a reduction, and that the building's rent is $400 per month and has not increased over time?

Leasing is a contract permissible in Islamic law by the Qur’an, Sunnah (definition), and consensus (Ijma’). Its conditions for validity are that the duration and the rent must be known, and the benefit derived must be permissible in Islamic law.

A trade name is a financial right that can be disposed of by sale or lease. If it loses its value, it is not entitled to rent. The rent for a restaurant is determined by agreement between the parties at the time of the contract and its renewal.