Easy-to-use Texas rental application forms. Save time and keep your records safe and easily accessible with RentSpree's online rental application for Texas.Applicant's name (as listed on proof of identification). Applicant's former last name (if applicable). E-mail. Your rental application is your opportunity to stand out amongst other applicants, so pay attention to spelling and grammar. Has Applicant ever: been evicted? A Texas rental application enables landlords to obtain the background information of lease applicants before authorizing a residential tenancy agreement. There is not one single rental application form you can download from a website. Each applicant must fill out a separate rental application. Applicants must submit a completed application form along with supporting documents such as proof of income and a security deposit.