Allah (Azza wa Jall) says in the Suhufan Mutahharah:
هُوَ سَمَّاكُمُ الْمُسْلِمِينَ مِن قَبْلُ وَفِي هَـٰذَا لِيَكُونَ الرَّسُولُ شَهِيدًا عَلَيْكُمْ وَتَكُونُوا شُهَدَاءَ عَلَى النَّاسِ
He it is Who has named you as Muslims both before and in this (Book), that the Messenger be a witness over you and you be witnesses over mankind (22:78)
Here Allah has claimed that the name “Muslim” has been given even before the present Revelation (of the Qur'an).
I would like to give all Muslims the good news that I have discovered the text in which the name Muslim has been given before the revelation of the Qur'an.
In the Book of Isaiah, chapter 42, verse 19, it is written:
מִ֤י עִוֵּר֙ כִּ֣י אִם־עַבְדִּ֔י וְחֵרֵ֖שׁ כְּמַלְאָכִ֣י אֶשְׁלָ֑ח מִ֤י עִוֵּר֙ כִּמְשֻׁלָּ֔ם וְעִוֵּ֖ר כְּעֶ֥בֶד יְהוָֽה
Translation: Who is blind, but my servant? or deaf, as my messenger that I send? who is blind as he that is at peace with me, and blind as Jehovah's servant? (Isaiah 42:19, American Standard Version)
The Hebrew word used in this verse is Měshullâm which is the Hebrew equivalent of the Arabic Muslim. I have reproduced quotations from several Bible commentaries which affirm this fact:
The meaning of the Heb. měshullâm (a proper name in 2 Kings 22:3; Ezra 8:16, and often) is uncertain. Many take it as the equivalent of the Arabic “Moslim,” = “the surrendered one” (Cheyne, Comm.). It is no objection to this that it is based on an Aramaic use of the verb (commentary of Cambridge Bible for Schools and Colleges)
The Hebrew meshullam is interesting, as connected with the modern Moslem and Islam, the man resigned to the will of God. (Ellicott's Commentary for English Readers)
The word used is connected etymologically with the Arabic muslim (our "Moslem") (Pulpit Commentary)