FAQ:Should we publicly expose false teachers?
Should we publicly expose false teachers and wolves in sheep's clothing?
Is this part of what we should do based on the scripture:
Romans 16:17-18 KJV  Now I beseech you, brethren, mark them which cause divisions and offences contrary to the doctrine which ye have learned; and avoid them.  For they that are such serve not our Lord Jesus Christ, but their own belly; and by good words and fair speeches deceive the hearts of the simple.
I would claim that the answer is no.
We should definitely discern who is who and avoid wolves in sheep's clothing but if we expose them publicly we break other scriptures.
Romans 12:18 KJV  If it be possible, as much as lieth in you, live peaceably with all men.
2 Timothy 2:24 KJV  And the servant of the Lord must not strive; but be gentle unto all men, apt to teach, patient,
Matthew 10:16 KJV  Behold, I send you forth as sheep in the midst of wolves: be ye therefore wise as serpents, and harmless as doves.
Exodus 23:7 KJV  Keep thee far from a false matter; and the innocent and righteous slay thou not: for I will not justify the wicked.
Rather than publicly expose the false teachers we should discern who is a false teacher and avoid him.