The argument identifies a real linguistic connection: Elijah's Hebrew name, Eliyahu, is commonly understood as "My God is Yahweh." But that does not make "Yahweh" the only permitted name of God, nor does declining to use that particular form break Islam's continuity with the prophets.
What the argument is claiming
The strongest form of the objection is this: the Quran honors Elias (Elijah) as a righteous prophet, and Muslims say that all prophets worshipped the same God. Yet Elijah's own name explicitly confesses Yahweh as God. If Muslims refuse to call God Yahweh, critics say they have either abandoned the God of Elijah or are using a different deity under the name Allah. They also argue that no Quranic verse specifically forbids Muslims from saying Yahweh.
A prophet's name does not define the limits of God's names
Elijah's name is a personal name containing a reference to God. It is not a revealed command that every later community must use that exact Hebrew form in worship. Many biblical names contain forms of divine names, but their presence in a person's name does not establish a universal liturgical vocabulary.
And Zechariah, John, Jesus, and Elias - all were of the righteous.
Quran 6:85
The Quran confirms Elias as a prophet. It does not require Arabic-speaking believers to reproduce the Hebrew wording of his name, any more than it requires Muslims to pray in Hebrew because Abraham, Moses, or David received revelation in earlier languages.
There is also a linguistic issue. The ancient Hebrew divine name was written YHWH, while "Yahweh" is a scholarly reconstruction of its pronunciation. Its exact ancient vocalization is not certain. By contrast, Allah is the Arabic proper name used by the Quran for the one God. Arabic-speaking Jews and Christians also use "Allah" for God, which shows that the word itself does not name a separate deity.
What "no distinction" actually means
The Messenger has believed in what was revealed to him from his Lord, and so have the believers. All of them have believed in Allah, His angels, His Books, and His messengers, saying, "We make no distinction between any of His messengers."
Quran 2:285
This means Muslims do not reject some true prophets while accepting others, or deny the revelation God gave them. It does not mean that every prophet used the same language, title, or form of worship. The Quran itself says:
To Him belong the Most Beautiful Names. Whatever is in the heavens and earth glorifies Him.
Quran 59:24
Classical scholarship therefore treats God's revealed names as names to be affirmed as revelation teaches, while recognizing that divine reference can be translated between languages. Muslims may discuss YHWH as the biblical designation, but Islamic worship uses the names taught in the Quran and Sunnah, above all Allah.
So the objection establishes a connection between Elijah and the name YHWH. It does not establish that Muslims worship another God, that Allah is absent from the prophets' faith, or that Muslims are forbidden from acknowledging what "Yahweh" refers to.