Tichá Noc is the name of a song and it means 'silent night'. Ticho means 'silence' in the Czech language. Well, the surname Tichy is also an Italian surname, which created confusion, but this Italian surname with variants Tecchio and Ticchini and many more is highly likely a patronym meaning 'son of Ticho', where Ticho is a firstname derived from the greek
tychon , which means 'coincidentially, perhaps'. I don't think these surnames are related to each other, although it's possible that the Czechoslovak surname Tichy (it is also used in Slovakia) could mean 'son of Ticho'. But
ticho means 'silence' in the Czech (and Slovak) language.
Tichy might mean 'from Ticha', where there could be referred to the river Ticha (Orlice). It might also mean 'from silence' or 'silent'.
Some links:
http://www.houseofnames.com/xq/asp.familycrest_details/s.Tichy/Tichy_family_Crest/Tichy_coat_of_arms/qx/Tichy.htm (about the Italian surname Tichy)
http://www.google.nl/search?hl=nl&ie=ISO-8859-1&q=ticha+silent&lr=
(links that prove that
ticha means 'silent')
About the rivers Ticha Orlice and Divoka Orlice:
http://www.google.nl/search?hl=nl&ie=ISO-8859-1&q=ticha+silent+orlice&lr=
(this link shows that
Ticha Orlice means 'silent eagle' and that
Divoka Orlice means 'fierce eagle')
note: Divoka is also used as a firstname, with the same meaning off course.