I will try my hardest to avoid making any further mistakes to avoid your collective internet wrath.
Your best bet in getting into esl teaching is to avoid internet forums as they are host to a lot of unhelpful people. This forum has a few members that try to complicate things - same goes for esl cafe.. Instead, come to poland and hit the pavement with your CVs, ideally in the summer.
Will having a foreign name help me or hinder me?
I don't think so.
I never had any problems, in fact my fairly good knowledge of the polish language helped me make connections and made a lot of administrative things easier after getting hired at a school.
For instance, i always had a plethora of students for private lessons as i was able to easily tap into people who could not speak a single word of english (imagine someone like that calling a non-polish speaker to arrange a private lesson).
Also, at the first school i at worked for, most of the administrative staff could hardly speak english so most meetings/communication was conducted in polish. I met many polish-americans/canadians/aussies during my time as an esl teacher, none of them had problems - even with first names like Przemyslaw;)
And remember, if you can't find work in the large cities, head out to smaller cities/towns.