A: To answer both questions: YES!
Your question is a matter of wording and language. As in, wanting to "glorify" God's name is an verb and "glorified" is an adjective.
The act of glorifying God is a reaction to the way the Gospel has penetrated our hearts. Another way of thinking about this is "representing God's name." We are Christians - as in we follow Christ. If we adhere to this, than we need to represent Him in what we say and do.
To "glorify" God is also an attitude. It means that we are humble in what we are doing and never point to our own ability, but to God who gives freely. In that, we are putting God first, thereby glorifying Him above ourselves.
You are also right to point out that His name is already glorified. If our God is a God who could create the world and everything in it, I'm sure that He could glorify Himself if He wanted to. But I believe that God wants to partner up with us and give us an opportunity to share in this joy. Hence, giving us Christ and a second chance for a relationship with Him.
[Answered by Pastor KJT]