My step daughter have my surname

Hi Distinguish Advocates, My wife have given birth to a girl in 2001 and from 2002 her husband abandoned them and left. His whereabouts are unknown. She file for divorce or anything just took care if the baby. But in 2009 our elders suggested a marriage between me and my wife. So we got married in June 2009. After that when the kind came to my home along with mother I have given my name as father and her initial as ' B '. Her biological surname and mine both starts with B so till the situation of taking a passport the surname was never expanded. Now she have my surname in her passport. In the year 2011 her mother with advise from an advocate applied for divorce and got exparte as her ex is missing from their life's. Now the question is I want to send my daughter to abroad for higher studies.. What issues my cone up for her while mentioning the details in applications.. Do I need to get any adoptions deeds done. Or Do we need to get the father's name removed from her birth certificate.please advise.