One of the big debates in Biblical scholarship is the dating of Isaiah. The consensus position tends to be that there were at least 2:and possibly 3 authors. The first author would then be presumed to have written in the 7th century BC and the later authors during or post exile.
Often this position is dismissed as just liberal with a suggestion that it only arises because people don’t believe in prophecy. However it is a bit more complex than that. A key issue is the specific naming of Cyrus in Isaiah 45. Whilst Biblical prophecy accurately foretells the future, the specificity of naming an individual seems to be unique here and raises the questions about why.
One possibility is that God does for a specific reason name a future person here. If so, we would want to pause and ask why. Perhaps the intention here is to get us to pause and pay attention to a significant text.
Another possibility is that we do in fact have one prophet called Isaiah but, as with others like Jeremiah, an editor has structured and redacted his material into the form we find it in Scripture. If so, it is possible that the author would have amended names in some places to show fulfillment just as a modern editor might change the name of New Amsterdam to New York in older texts.
I don’t think that it is necessary to posit 2 or 3 author theories to account for Isaiah and there are potential problems with this. However, nor does the possibility that the text was developed at a later date undermine belief in inerrancy or prophecy.