The word Muslim in Arabic is an active participle. It comes from the simple verb salima, which means to behold and the fourth form of that verb, aslama, means to give something up, to surrender. A Muslim is the one who does that action. This is the active participle and we understand that to mean that we're surrendering ourselves to God.
Essentially, the Muslim is a submitter to God. The sense of this can be seen already in all of the previous scriptures.
For example, in the Bible, we are shown that Abraham submitted to God. He was faithful and he carried out God's commandment. We also have Jesus in the New Testament in Matthew's gospel chapter 26, verse number 39. He fell on His face, prayed and said, "Not my will, but yours be done." He is surrendering Himself to God and submitting to the will of God.
It seems that the word is also there in at least one passage of the Bible in Isaiah chapter 42, verse number 19. Mushafiq Sultan from Al-Mawrid Institute has a video on this, specifically. Several commentaries on the Bible bring out this meaning. For example, in a commentary entitled "Concise Bible Commentary" by Reverend Lowther Clarke, there is a reference to Isaiah 42, verse number 19, where the Israelites are set to be the messenger of God to the other nations and yet they are said to be blind. Here, the verse says, “The messenger to the Gentiles is blind to his destiny. He ... with me. The Hebrew consonants are MSHLM, reminding us of Moslem. Devoted one is approximate to the meaning.” Many other commentaries mentioned this connection between the words “Meshullam” here and “Muslim”.
Sometimes they mention it, but they pass over it and say that it doesn't mean exactly that. However, we can see the correspondence between the Hebrew word there and the Arabic word Muslim.
One obvious difference is that the sin sound of the Arabic has changed into the shin sound of the Hebrew, but this is normal. For example, when we say Salaam, in Hebrew it is Shalom. So the sin gets changed to the shin.
We also have Ellicott's commentary on the Bible and it essentially says the same thing. It is written that “The Hebrew meshullam is interesting, as connected with the modern Moslem and Islam, the man resigned to the will of God.” We also have the equivalent of the word Allah. Allah in Arabic means something like “the God”. This seems to correspond closely to the Hebrew Elohim, which occurs in Genesis 1:1, wherein the Arabic translations of the Bible, it is described that in the beginning, Allah created the heavens and the earth. The ideas are there and even the wording is there, but sometimes the wording gets lost in translation.