Texas Penal Code, Title 8, §38.02:
Failure to Identify.
(a) A person commits an offense if he intentionally refuses to give his name, residence address, or date of birth to a peace officer who has lawfully arrested the person and requested the information.
(b) A person commits an offense if he intentionally gives a false or fictitious name, residence address, or date of birth to a peace officer who has:
(1) lawfully arrested the person;
(2) lawfully detained the person; or
(3) requested the information from a person that the peace officer has good cause to believe is a witness to a criminal offense.