The parties, who were not named due to South Africa's child protection laws, both filed papers in the Durban High Court in the matter which will be heard by a judge on Friday.
The father, a 40-year-old Hindu information technology professional, has asked the court to order that his two-year-old son's surname be registered in official records as his and not the mother's, as is the case at present.
In opposing papers, the Muslim mother has claimed that the father is playing a "tug-of-war" game with their son over the name.
The couple entered into a Muslim marriage after the father converted to Islam, but the marriage was ended in 2005 after he found it difficult to adapt to a Muslim lifestyle.
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He undertook the traditional utterance of the word "Talaaq" three times to end the marriage, after which he returned to Hinduism.
"We resumed our relationship around 2008. She fell pregnant in October 2011 and our son was born in September 2013," the father said in court papers, adding that he was not happy to have his son assume a Muslim surname, as he loved him dearly.
"I have been advised that a child born out of wedlock automatically carries the mother's surname," the mother said in an affidavit.
"My son has settled in nicely with me and my family. I am loathe to trigger any confusion in his mind concerning the surname," she added.
Legal experts favour the mother, concurring that while this would be the first case of its kind in South Africa, the father stood a very slim chance of winning the case.