First of all, I’m sure everybody here knows someone who started out shy and “came out of their shell”. This is part of why parents make shy kids take performance-type classes or do confidence-building activities with them.
We certainly know this happens with Christ. It’s one of the oldest Christian stories – the person who becomes “bold”.
Of course, most shy people will always be a bit shy, because God doesn’t always throw His power around and because grace builds on nature. But as a person grows more experienced and wise, a shy person can turn that into a strength of being perceptive and sensitive to others, or of having independence in their thoughts and actions. And God is fully supportive of that.
Then again, it may always be a problem, designed to test you and strengthen you. But you may be able to strengthen other aspects of yourself, so that being shy doesn’t matter so much.
But that’s no shame. Jesus’ wounds didn’t go away when His Body became glorified; they became signs of His glory and love.
So yes, God will change you, but there’s no way to tell how or what He’ll choose to change. The more you work hard to change yourself and improve your character, and the more you strengthen your virtues and conquer or work past your weaknesses, the more He’ll delight to change you. The less you respond and take initiative to do His will, the less you’ll change, barring a miracle or serious trouble and trial.)