The Quran does not identify Mary the mother of Jesus with Miriam the sister of Moses. The objection rests on a real verbal resemblance, but it turns that resemblance into a historical confusion too quickly.
Why the charge sounds plausible
The critic is not inventing the question. The Quran says to Mary:
"O sister of Aaron, your father was not an evil man, nor was your mother unchaste."
Quran 19:28
It also calls her:
"Mary, the daughter of Imran, who guarded her chastity..."
Quran 66:12
Since Miriam in the Bible was the sister of Moses and Aaron, and their father was Amram - Arabic Imran - the critic argues that the Quran has merged two women: Miriam of the Exodus and Mary the mother of Jesus. Stated strongly, the objection says: if Mary is called sister of Aaron and daughter of Imran, the simplest reading is that she belongs to the same immediate family as Moses, which would be an anachronism.
The Prophet's own explanation
This exact question was asked during the Prophet Muhammad's (PBUH) lifetime. Al-Mughirah ibn Shu'bah reported that when he went to Najran, the Christians there objected: "You recite, 'O sister of Aaron,' while Moses was before Jesus by such-and-such a time." He asked the Prophet (PBUH), who replied:
"They used to name themselves after their prophets and the righteous people before them."
Sahih Muslim
That answer matters. It shows that the phrase was not understood by the Prophet (PBUH) as meaning Mary was literally the sister of Moses' brother. Names like Aaron and Imran could be reused among Israelites, just as Muslims later reused names like Muhammad, Umar, Ali, Fatimah, and Aisha. A woman could be linked to a man named Aaron, or to an Aaronic family, without being the ancient Miriam.
Arabic also uses "brother" and "sister" more widely than biological sibling. A person may be called the brother of a tribe, the sister of a lineage, or a member of a religious house. This is not special pleading; it is normal Semitic and Arabic usage.
"Daughter of Imran" does not force the critic's reading
The critic's strongest move is to say: even if "sister of Aaron" can be figurative, "daughter of Imran" makes the identification unavoidable. But that only works if Imran must be the one and only Amram of Moses' family. The Quran itself presents this Imran in the story of Mary's birth:
"When the wife of Imran said, 'My Lord, I have vowed to You what is in my womb, dedicated...'"
Quran 3:35
Then the child born is Mary:
"And when she delivered her, she said, 'My Lord, I have delivered a female'..."
Quran 3:36
The Quran is not placing Mary in Pharaoh's Egypt. It places her with the mother who bore her, with Zakariyya as her guardian, and with Jesus as her son. The narrative world is unmistakably the first-century setting of Mary, not the time of Moses. The repeated name Imran is therefore best read as the name of Mary's father, not as a claim that she is Moses' sister.
What this does and does not establish
The objection establishes that the Quran deliberately uses names associated with priestly Israel: Aaron and Imran. It also establishes that the wording can sound surprising to readers who assume every kinship term must be literal and every repeated name must refer to the same person.
It does not establish a historical error. The Prophet's (PBUH) own explanation, ordinary naming practices, Arabic kinship usage, and the Quran's separate placement of Moses and Mary all point away from confusion. The Quran links Mary to a noble Israelite religious line; it does not mistake her for Miriam of the Exodus.
So the charge is understandable as a question, but too weak as a proof. It depends on reading the Quran in the narrowest possible way while ignoring how the language was used and how the Prophet (PBUH) explained it.