In high school, between 1984-1988, I read a sci-fi fantasy book about a sorceress with purple hair. She had a son and was fighting an evil wizard. She had to learn the secret name of magical creatures and, if she says their names, she has control over them.
"Purple hair" rings no bells at all, but aside from that the description fits Patricia McKillip's "Forgotten Beasts of Eld" (1974). Sybel (ivory hair, not purple) lives in an isolated retreat where she cares for and is gradually adding to a menagerie of magical creatures. She researches each creature through associated legends and folk tales, then summons it to her by calling its name in her mind.
There is an on-going dynastic war going on in the kingdoms around her; at some point prior to the start of the book a young man fleeing that war arrives at her refuge carrying with him an infant named Tamlorn who may or may not be the son of Sybel's sister. He leaves Tamlorn in Sybel's care, and she agrees to raise him. At some point one of the warring kings becomes convinced that Sybel is a threat to his power and hires a wizard to essentially enslave her by controlling her mind. He fails, but the attempt so enrages Sybel that she starts plotting revenge on the king.