§ 37.03. Aggravated Perjury
(a) A person commits an offense if the person commits perjury as defined in Section 37.02, and the false statement:
(1) is made during or in connection with an official proceeding; and
(2) is material.
(b) An offense under this section is a felony of the third degree.

§ 37.06. Inconsistent Statements
An information or indictment for perjury under Section 37.02 or aggravated perjury under Section 37.03 that alleges that the declarant has made statements under oath, both of which cannot be true, need not allege which statement is false. 
At the trial the prosecution need not prove which statement is false. Impeachment by contradiction

"feigned ignorance”

Turncoat witness: A witness who flips or undermines their own prior testimony/statements by suddenly claiming ignorance. 
law.temple.edu

Evasive or non-responsive testimony: Broader category that includes this; repeated "I don't recall" can lead to sanctions (e.g., contempt in depositions) if the court finds it obstructive. 
litedepalma.com

Selective/convenient amnesia: Informal but frequently used by lawyers to describe it in court. If prosecutors can prove the witness knew at the time they made the first statement that they had no personal knowledge (i.e., they knowingly made a false statement with intent to deceive), then the conduct can be charged as perjury or aggravated perjury.