Why isn't Shimson's mother named in Pesukim that tell the story? She is featured rather prominently, and the angel appears to her before speaking with both her and Manoaḥ. It would stand to reason that she is as important a character as other barren mothers who prayed for children and were blessed with great leaders for sons. (Aside, to preempt comments comparing Shimson to some of those other leaders: Perhaps he wasn't the greatest leader or a true Navi, but he was great enough for his story to appear in TaNa"Ch, and it's not like his father isn't named.)
To answer the minim (people who deny the oral Torah) because the names of important people such as Dovid's mother or Avraham's mother is also not mentioned in the Torah is brought down through oral tradition which minim do not have(based on Bava Basra 91a).
Rabbi Chaim Navon in this class suggests that she wasn't named to symbolize that Shimshon ultimately followed in the footsteps of his father Manoach in terms of worldview and his view of his path as a judge. We see that after discovering that an angel appeared and spoke to them, Manoach was afraid that they would die. This suggests a mythic view of the world: When lowly mortals meet higher entities, the lowly mortals cannot hope to withstand the full might of the higher entities and are annihilated. Manoach's wife, on the other hand, says that if Hashem - the higher entity - wanted to kill them, He would have done so already. In other words, she understood that Hashem is interested in a dialog with man and has a plan for mankind, not merely interested in using man as a pawn or a toy. That Manoach had a lower understanding of the relationship between man and his Creator may be hinted in the words of the gemara (Brachot 61a):
"Manoah was an ignoramus..."
Shimshon, as a judge, was given a choice: To see the bigger picture, to see his role in Hashem's master plan, or to maintain a narrow, mythic view of the world, like the Plishtim he enjoyed hanging around. Would he choose to see that his strength was a gift from Hashem to save Yisrael, or would he choose to see his strength as an attribute related to his status as a mythologic super-strong demi-god like person who acts only out of self-interest?
In his early years, Shimshon at times followed one path while at other times followed the other. Eventually, his downfall came because he embraced the latter path: That of a supernatural self-serving demi-god. He slightly redeemed himself at death by finally realizing his strength came from Hashem when he said (Shoftim 16:28):
"Then Samson called to the LORD, “O Lord GOD! Please remember me, and give me strength just this once, O God, to take revenge of the Philistines, if only for one of my two eyes.”"
However, his mother remained unnamed, because even she had eventually become convinced of the truth of Manoach's path, as it says (Shoftim 14:4):
"His father and mother did not realize that this was the LORD’s doing..."
Even Shimshon's mother didn't realize that what was happening to her son was part of Hashem's plan. This suggests that she lost sight of the truth, of there existing a great plan for man; she too became entangled in the mythic view of the world.