Review the terms and conditions of your lease agreement to determine if the landlord has violated the agreement in some way. Examples include failing to make repairs related to safety and comfort, such as a hole in the roof or a broken furnace in the dead of winter. Follow the same strategy if you are trying to remove your name from some other type of lease agreement.
Consider other terms in the agreement including early termination clauses, if applicable. Early termination allows termination of the entire lease with notice and a penalty fee. That allows you out of the lease but forces roommates to move or sign a new lease. Roommates must agree to any change in the lease affecting them, including financial responsibility for the remaining terms on the lease.
Contact a real estate attorney to review legal grounds for removing your name. Free legal assistance is sometimes available from a local legal aid office or similar nonprofit organization. Find contact information in your area by calling the public library.
Write a letter based on your review of the lease and consultation with the attorney. If no legal options are available, tell the landlord in the first paragraph that you wish to remove your name from the apartment lease agreement within the next five business days. State emphatically and clearly in the next paragraph that because of personal reasons you cannot and will not remain in the apartment.
State in the third paragraph that you wish to negotiate an agreement that is fair and allows removal of your name from the lease. Also state that you have consulted with an attorney but wish to settle this amicably.
End the letter by asking the landlord to contact you to discuss a reasonable solution.