Would it be morally wrong for me to allow another man to remain my child's legal father?

My oldest child moved in with me at age 7 after her mother died. She was born when I was young and dumb and she never laid eyes on me before that day. Time has passed.She is happily settled in with myself, my wife,and 2 sons and turned 10 in September. The only problem now is culture wise.
I am a Russian National as is my wife and our 2 sons are dual citizens. My eldest child had an American mother and her mother's estranged(when she was born) husband is named as her father on her birth certificate. He is Dominican. My eldest child is a dual American/Dominican Citizen. In the beginning I left the legal stuff as it was,but now I want to visit my homeland and cannot get my own child a Russian Passport.
I wanted to change her name to something I could actually pronounce and my own surname, but she objected quite vocally and said she liked her current name fine. Now a lawyer is telling me I cannot just file and change her name. My wife and myself MUST adopt her according to Utah Laws in order to straighten out all the legal jargon. Meaning I must somehow track down her mother's ex-husband and convince him to sign away his "rights". Her mother had him providing financial support until the divorce was final and I have reason to suspect he will not sign. Even DNA will not bypass this,because he has been her legal father for 10 years.
I have the money to finance the legal proceedings in Savings,BUT my wife is against taking the matter to court,because
1.My child will likely prefer to KEEP her Dominican Citizenship due to being biracial and not identifying closely with our culture.She's learned Russian,however isn't interested in much else.

2.My child is satisfied with her name.

3. Taking her to Russia in the wake of the recent political climate is not a good idea.

In a nutshell my wife believes the money will be wasted. I have not yet broached the subject of a name change again with my child, because as I said before she was very vocal about liking the name her mother gave her even if she has another man's surname. If I do not go through with the legal proceedings I will still have Sole
Legal and Physical Custody,but my child won't have my surname or be able to obtain a Russian Passport.

My child is happy and that's is wonderful,however I am NOT happy. I want her to be completely mine! My wife says it's just my ego and I am selfish though.