We pray to a merciful Savior who despised the shame in order to cover our shame.
So, we should pray shamelessly.
Check out this quote by Alexander Whyte I read here:
See the man at midnight [described in Luke 11:5-8]. Imitate that man. Act it all alone at midnight. Hear his loud cry, and cry it after him. He needed three loaves. What is your need? Name it. Name it out loud. Let your own ears hear it. . . . The shameful things you have to ask for. The disgraceful, the incredible things you have to admit and confess. The life you have lived. The way you have spent your days and nights. And what all that has brought you to. It kills you to have to say such things even with your door shut. Yes, but better say all these things in closets than have them all proclaimed from the housetops of the day of judgment. Knock, man! Knock for the love of God! Knock as they knock to get into heaven after the door is shut! Knock, as they knock to get out of hell!”Whoever puts their trust in him will not be put to shame!
They will be put to shame and even humiliated, all of them; The manufacturers of idols will go away together in humiliation. Israel has been saved by the LORD With an everlasting salvation; You will not be put to shame or humiliated To all eternity. (Isa 45:16-17, ESV)
For in Scripture it says: "See, I lay a stone in Zion, a chosen and precious cornerstone, and the one who trusts in him will never be put to shame." (1 Pet. 2:6, NIV)