It depends on whether the father would be considered a parent. The father is the child's biological father. Has there been a blood-test to determine the child's actual father? If the father gives consent than you should have absolutely no problem.
The court could order the ex-boyfriend to submit to a blood test to determine whether or not he is the biological father. If ex-boyfriend is the father, than his consent to the name change is required. If not, and it cannot be determined who the father is, than the judge might just allow the name change. Best of luck. Please contact a family law attorney for legal advice.
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