When I first started out, it was on my mind a lot, too. ie... if I'm not from a certain ethnic group, and their ethnicity is part of the name of the church, will they be wondering, what are you doing here? Why would you come here? No ancestral ties, etc???
I have ended up at a GOC, and feel at home. 'Am not one ounce Greek. Now, instead of feeling "different", I find it so thrilling they share so much of their culture, etc...and are so warm. Yes, I get the question at times, are you?
?? Did you marry a Greek? etc.... but my answer is, no, I am here because I believe this is the true church. Oh!!! they say, and smile.
If they are Orthodox, you can answer to any ethnic group this way!
The Liturgy is half Greek, half English. To be honest, I wouldn't last in one that didn't have some English. So, I can definitely see that as a decision for people seeking.
What worked for me was to join small ministries within the church, and bonds grew that way. I forget I'm not Greek!
Pray that God shows you where He wants you. I didn't even know about this church, and found out about it one day, and visited. Give each one some time, because you will grow and change and eventually you will know where you should be. If I stopped after only one or two visits, I wouldn't have this now. You need to develop an overall picture. It takes time.
God may surprise you!