Ha-SHaKH, Shabtai ben Meir ha-Kohen, also referenced as Reb Shabsai HaKohen Katz,
was a prominent Rabbi who was active in Holešov during the 17th century,
and was known as an eminent 16th Century interpreter of Jewish law.
Rabbi Shakh came from Vilnius and lived in Holešov until his death in 1663.
He was known as Shakh, from the Hebrew initials of his work Sifsei ha-kohen (literally “Lips of the Priest”),
which is recognized as one of the most basic and authoritative commentaries on the Shulchan Aruch.

The word "mundes" is present in the German language,
and is translated to English as "mouth",
as you can see for yourself by using Google Language Tools.
Assuming that mouth and lips can be considered one and the same:
The addition of mundes to Shakh is explained by the fact that
Shakhmundes means Priest's Lips.

One can only conclude that the name Shakhmundes is of the same etymology as Shakh,
if not more-so.

Rustran.com translates the Russian "Шах" as "Shah", which can found in Dictionary.com.
Other common interpretations of Шах/Shakh/Shah include "king" and "ruler".
Further translations and historical information of "Shah" can be explored on Webster's Online Dictionary [The Rosetta Edition™].

Links

Daniel Shakhmundes

Lev Shakhmundes