For instance, in Isaiah 43:1-5, change the words of "Jacob" and "Israel" to your name. "But now thus says the Lord, he who created you, O (your name), he who formed you, O (your name): Do not fear, for I have redeemed you; I have called you by name, you are mine." A couple of other verses that work well with this form of prayer are Isaiah 54:4-14 and I Corinthians 13:4-8 (by putting your name in the place of the word "love").
May your prayer time bring a strong connection between you and your Creator.