Lease agreement requirements

[Hiren Patani]

Does all the tenant who would be occupying the property have to sign the lease agreement in the state of Texas? 

I have a potential tenant who will be living with her son. Mother is responsible for paying the rent. Is there a clause or TREC requirements that both mother and son has to sign the lease agreement? 

Note: I'm (landlord) is talking directly with tenant agent and the agent is saying only primary applicant (i.e. Mother) is require/responsible to sign the lease agreement.

Thanks!!!