The American Civil Liberties Union of Georgia sued last month on behalf of Elizabeth Handy and Bilal Walk, who had chosen the name ZalyKha Graceful Lorraina Allah.
The group said it is dropping its lawsuit because the Georgia Department of Health has issued a birth certificate with the name the couple had chosen.
"This is an important vindication of parental rights and a long overdue victory for Elizabeth and Bilal," ACLU of Georgia Executive Director Andrea Young said.
Now that the 23-month-old child has a birth certificate, her parents, who are expecting another child in July, can get a Social Security number for her, which will make it possible for them to access medical coverage and enroll her in public school, Young said.
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A Department of Public Health lawyer had argued state law requires a baby's surname to be that of the father or the mother for the initial birth record. They said the last name of the child, who was born in 2015, should either be Handy, Walk or a combination of the two.
Young urged any other parents who may find themselves in a similar situation to reach out to the ACLU of Georgia.