The answer is both "yes" and "no." Everybody has secrets, and the Bible tells us that this is okay, especially when it comes to private matters and confidences that others share with us.
Matthew 6:3-4 Matthew 6:3-4  But when you do alms, let not your left hand know what your right hand does:
 That your alms may be in secret: and your Father which sees in secret himself shall reward you openly.
American King James Version×, 6 and 17-18 tell us some of the things that should be kept secret from others.
"But when you do a charitable [kind] deed, do not let your left hand know what your right hand is doing, that your charitable deed may be in secret; and your Father who sees in secret will Himself reward you openly...
"But you, when you pray, go into your room, and when you have shut your door, pray to your Father who is in the secret place; and your Father who sees in secret will reward you openly...
"But you, when you fast, anoint your head and wash your face, so that you do not appear to men to be fasting, but to your Father who is in the secret place; and your Father who sees in secret will reward you openly."
Proverbs tells us that there are advantages to being able to keep secrets (confidences). In Proverbs 11:13 Proverbs 11:13A talebearer reveals secrets: but he that is of a faithful spirit conceals the matter.
American King James Version×we read, "A gossiping fellow will betray secrets, but a trustworthy man [person] will keep a confidence."
Then in Proverbs 20:19 Proverbs 20:19He that goes about as a talebearer reveals secrets: therefore meddle not with him that flatters with his lips.
American King James Version×it says, "Talebearers [gossips] let out secrets; have nothing to do with a gossip" (Moffatt translation). People who can keep confidences are described as being trustworthy, but those who don’t are called "gossips" or "talebearers."
But what about having secrets from God? To answer this we need to go to some examples in the Bible. Sometimes we do things in life that we don’t want anybody to know about. Can we hide things or have secrets from God?
David told his son in 1 Chronicles 28:9 1 Chronicles 28:9And you, Solomon my son, know you the God of your father, and serve him with a perfect heart and with a willing mind: for the LORD searches all hearts, and understands all the imaginations of the thoughts: if you seek him, he will be found of you; but if you forsake him, he will cast you off for ever.
American King James Version×, "As for you, my son Solomon, know the God of your father, and serve Him with a loyal heart and with a willing mind; for the LORD searches all hearts and understands all the intent of the thoughts."
In 2 Samuel 12:12 2 Samuel 12:12For you did it secretly: but I will do this thing before all Israel, and before the sun.
American King James Version×David tried to hide his acts from God, but try as he might he couldn’t. "For you did it secretly, but I will do this thing before all Israel, before the sun," God responded.
When we try to hide things from God, they are usually actions or thoughts we need to repent and ask God to forgive us of. This is what David did in verse 13 of 2 Samuel 12 and Psalm 51. But even after doing this, he had to suffer the penalty of his wrongdoing (see verse 14 of 2 Samuel 12).
So there are some secrets we need to keep. But try as we might, we are not able to keep anything secret from God. If we have been trying to hide things from Him, we need to change our ways (repent). VT