In my opinion, Grendel's mother plays something of an anomalous role if you think of her as a female rather than simply as a monster.
As you point out, she has no name. You can argue that this is emblematic of the position of women in those days. They were always either somone's daughter or someone's wife or someone's mother. She, like them, has no real identity of her own.
On the other hand, Grendel's mother plays a part that is not in keeping with her sex. She takes revenge for her son's death and she does it in a very lethal way. So this seems to contradict the idea that her namelessness is an intentional thing -- something that is meant to show the proper role of women in society.