Will God give you a new name?

There are certainly times in the past that God is known to have re-named people (Abram to Abraham and Saul to Paul, for example) but in terms of a specific promise to give every believer their own name, there's an interesting passage in Revelation chapter 2 referring to this very matter. God does, in fact, say that those who "overcome" (stand faithful to God through the difficult time on Earth) He will give them "a white stone with a new name written on it, known only to him who receives it."

This comes up again in Revelation 3:12 where God promises, again to those who hold on to their faith in Him, that He will write three names on them, one of them being "my (God's) new name." The slightly difficult thing about these passages is that this section of Revelation is where God is sending very specific messages to a group of specific churches. He makes different promises to and requests of each one of them.

On the other hand, some of the things God tells these churches are not very different from things promised to all believers. It is debatable, therefore, whether or not the "new names" are promised to every believer or just specific ones. You may also want to look at Revelation 19:11-16 where Jesus is described as having a name written on him that only he knows. I would point out as well that God never says you couldn't have a special name, and if you so desire it I would simply try asking Him if He would give you one.

I think the apparent name changes quoted are more to do with language differences and translation. i.e. Aramaic to hebrew, hebrew to english and even middle english to modern english. (Mo'she for moses. Yeshwa for Jesus etc.)