There's  no  "documentation" for  the romanization of  Slavic names, personal or geographic, in  Hebrew or Yiddish contexts.  For  the time being,  the philosophy at  LC  is  to  try  to approach the sound of the original within the limitations of  the script  and  the  cataloger's knowledge.   Thus  the  (unwritten) policy  is  to  transcribe "Pyotr"  rather  than  "Piyotr."
The best-known name of this kind is "Byalik."

The NAF has several Russian authors with the surname "Kliatskin" (ligatures over both the "ia" and the "ts").
There are two "found romanizations" for authors with this surname--"Kliatzkin" and "Klatzkin."
Based on this LC leans toward "Klyatskin" for the "standard" romanization of "kof-lamed-yod-alef-tsadi-kof-yod-nun".
One can to consider alefs in spellings like this as matres lectionis for the vowel "a" rather than as "glottal stops" (as in "Kli'atskin") because there is nothing to suggest that the Russian name is pronounced with anything like a glottal stop.