Applicant's name (as listed on proof of identification). Applicant's former last name (if applicable). E-mail.The tenant will often be required to pay a non-refundable fee. We are requesting you to fill out this Supplemental Rental Application because you have indicated that you are not a U.S. citizen. We are asking all applicants. How to fill out a residential lease application in Texas? List all personal details accurately. A Texas rental application enables landlords to obtain the background information of lease applicants before authorizing a residential tenancy agreement. Gather the necessary paperwork you need to quickly complete the apartment application process and pay the required fees to secure your new apartment. Easy-to-use Texas rental application forms.