The word "vardan" now functions as a preposition meaning "for the sake of" or "in the name of".
Originally it is the illative case of the noun "vardas". The illative case, meaning "into something" is not part of the standard Lithuanian case system, but it's still used in fixed phrases and in Eastern Lithuanian dialects:
laivas > laivan (into the boat)
jūra > jūron (into the sea)
pilis > pilin (into the castle)