Does Keccak have an eTCR mode? On page 7 of NIST's views on SHA-3's security requirements and Evaluation of attacks, I see that, at least at this point, NIST planned on offering SHA-3 having eTCR security (defined on page 3):


  eTCR: Find $M$ and then for a randomly chosen $r$, find $M’$
  and $r’$ s.t. $H_r(M) = H_{r’}(M’), (r,M) ≠ (r’,M’)$ where
  $H_r$ is the randomized hash.


However, I never saw any subsequent references to the eTCR property for the SHA-3 candidates.

Does SHA-3 have an eTCR mode?
SHA-3 is conjectured to be collision-resistant, which is enough for $H(r \mathbin\| m)$ to be eTCR; if SHA-3 fell to a collision attack like MD5 and SHA-1 before it, it would nevertheless be surprising and remarkable and worthy of publication for SHA-3 to fall to a target collision attack as neither MD5 nor SHA-1 to my knowledge has, but one can only speculate about hypothetical developments past the failure of what is already only a conjecture.

The NIST-recommended ‘keyed hash’ function associated with SHA-3 is KMAC of NIST SP 800-185, of course.  If you're still not comfortable with that, the NIST-recommended randomized hash for collision-resilient signatures is RMX of NIST SP 800-106, which you could use with SHA-3 out of an abundance of paranoia, but I have never heard of anyone bothering to do that.