what does the name "polixenia" mean or translate to in english

Hi kauai-ga

I'm glad you chose Google Answers and am very happy to forage through
the web for Greek roots for you.

Polixenia is a combination of the roots "poly" (poli is the combining
form) and "xenia"

"poly" means  "many" or "much"
http://abasiccurriculum.com/homeschool/roots/athens/

"Xenia"  is the plural of "xenium" which literally means  "A present
given to a guest or stranger"

http://dict.die.net/xenia/

I also found a translation of "xenia" to mean "the hospitable one."

http://64.233.179.104/translate_c?hl=en&sl=de&u=http://lexikon.freenet.de/Xena&prev=/search%3Fq%3Dpolixenia%2Bdefinition%26num%3D20%26hl%3Den%26hs%3DsrT%26lr%3D%26client%3Dfirefox-a%26rls%3Dorg.mozilla:en-US:official

Using only the slightest poetic license you can consider Polixenia to
mean "very hospitable."

Polixena (a form of the name Polixenia) was, in Greek mythology, the
sister of the Trojan Hector who was killed by Achilles in the Trojan
War. Polyxena was a heroine to the Trojans, reputed to have either
given her gold bracelets to the army when it fell short of gold; or to
have given herself to the Greek Achilles, thus learning of his
vulnerable heel.  She of course would have passed on this intelligence
to the Trojan side.

http://www.stanford.edu/~plomio/polyxena.html

As you can see, the Trojan Polixena was not particularly hospitable
(unless you count offering herself to the "stranger" Achilles), but
she was heroic.

All in all, I'd say that Polixenia is a name rich with good connotations.

I wish you all the best, 

alanna-ga