I researched into this and found this page,
Yam suph – Hebrew words literally rendered ‘Reed Sea’
You should really visit the page for a detailed explanation on why the Hebrews called the Red Sea, Reed Sea.
Basically, reeds (freshwater plants) were seen on the shoreline of the Red Sea (saltwater). I assume that Moses and the Israelites did not have time to stop and taste the water to see whether it's salted or fresh. They saw fresh water plants outlining the shore hence, they knew it to be Sea of Reeds.
Names in biblical times and in Hebrew often symbolised a literal meaning rather then an exact location. One obvious example is the name Immanuel which means God with us. Does it mean the prophecy is fake because the Messiah's name was not Immanuel? No. So, just because the Red Sea today is not called the Reed Sea, it doesn't meant the Red Sea cited in the Bible is a mistranslation. I would think that modern people who translated the Bible found it easier to just put Red Sea because it is what it is.
Majority of the population (who read the Bible) do not study the Hebrew language. Hence, they would arrive at a conclusion that there is a mistake in the Bible (since there is no Sea of Reeds in modern context) when there actually isn't. What if this inhibits someone from Christ? It's not impossible. Now, the copyist wouldn't want that, would he?
The Reed Sea is the Red Sea today but the Reed Sea named by the Hebrew men is basically a literal perspective of what they saw. It is in no way a term for a literal location. One could even say it was a description, actually.