Hi Aylenna,
I will try to answer your questions briefly. First, yes you would have to have a Baptismal, or Christian name. You would be named in honour of an Orthodox Saint, who is an intercessor in Heaven for you. Your Priest might select one who he feels may be suitable for you. A lot of converts, if their name is thta of an Orthodox Saint keep their given name, e.g: Grand Duchess Elizabeth Feodorovna when she became Orthodox took the name of St Elizabeth the Righteous, mother of St John the Forerunner and Baptist.
Going by your name, it might be nice to choose St Helen (in Russian Elena). She was the mother of St Constantine the Great, who converted the Roman Empire to Christianity. St Helen was very pious and devout, and went to Jerusalem and among other things, discovered the Cross that Christ was crucified on. In fact just last week we had the Feast of the Elevation of the Cross which commemorates that event.
Next. You ask is the Ukrainian Orthodox Church the same as the Russian Orthodox Church. Yes. The Orthodox Church is the Orthodox Church wherever you go. There are Greek, Serbian, Arabian, Japanese, Romanian, Bulgarian Orthodox Churches and many others beside, which all share the same beliefs, doctrine etc. HOwever, you need to be sure it is a Canonical Orthodox Church. In the Ukraine itself, there has been a breakaway group which has a self-proclaimed Patriarch. That particular church, whilst calling itself Orthodox, is orthodox in name only as it has severed itself and is uncanonical. Find out if the Ukrainian Church in your town is under the Moscow Patriarchate. If it is a 'Unia' Church, then it is not Orthodox at all, but Roman Catholic, but retaining Orthodox forms of liturgical worship.
Finally, please, please, please do a lot of soul-searching and read as much as you can about the Orthodox Church before you get baptised. In some ways it is better not to have become Orthodox than to end up throwing the gift of Orthodoxy away at a later age. Orthodoxy is
serious Christianity. There is rigorous fasting for extended periods of the year. We have Confession where you examine your soul and all your actions minutely, but the Kingdom of Heaven is taken by the forceful. It is not the 'I'm baptised and Orthodox now, so I am saved!' type of Faith. It is serious and hard work. Through our lives here we attain our salvation, but everyday is a struggle to cleanse ourselves and to fight for the salvation of our souls against those that war against us (and not only the demons on their own, but devils working through other people.)
Orthodoxy is a beautiful, intensely spiritual Faith, and like anything worth attaining you have to work hard for it, but the 'rewards' are well worth the struggle. I recommend you look at the articles on the
www.fatheralexander.org website.