Analysis:
Was "Sunday" a nickname used by Mary Ann Bugg?

The only early references to Sunday as a nickname for Mary Ann Bugg are found in William Monckton’s Three Years with Thunderbolt.[1] Supposedly a memoir, this is in fact primarily a work of fiction crafted by writer Ambrose Platt after interviews with Monckton (see Review: William Monckton’s Three Years with Thunderbolt). 
    Monckton/Platt mentions Thunderbolt’s wife in the book and calls her Sunday. He is clearly referring to Mary Ann Bugg as he reports that Fred and Sunday had been together for a long time and had a family. Yet he never names Fred’s wife as Mary Ann and the woman he describes does not resemble Mary Ann Bugg in personality or in her life situation in 1868 when Monckton roamed with Thunderbolt. Fred and Mary Ann had seemingly broken off their relationship by the time Fred took up with Monckton, so it is likely the boy never met her. That being the case, the only logical conclusion is that the nickname Sunday was also part of Platt’s fiction. As Monckton probably never met her, he probably had trouble remembering her name, if he had ever known it. Contemporary newspaper reports merely called her Thunderbolt's half-caste or Mrs Ward or Captain Ward's wife (and so on) without recording her actual name. Giving her a meaningless nickname was probably the easiest way out.  
     Like Louisa Mason and Yellow Long, Sunday is just another of the erroneous nicknames that have been laid around Mary Ann's neck. No doubt she would be astonished if she knew. 
        

Sources:
[1] Three years with Thunderbolt  - published in the Daily Telegraph daily from 2 September 1905; see also Monckton, William Three Years with Thunderbolt, Cassell, Melbourne, 1907