KJV gives the clearer and stronger reading of original intent over the ESV.

Once again, no surprises here...

Profession versus Confession. Those weaker in the understanding of English and the etymology of these words may miss this but here we go none the less...

Fight the good fight of faith, lay hold on eternal life, whereunto thou art also called, and hast professed a good profession before many witnesses. 1 Timothy 6:12 KJV

VS:

Fight the good fight of the faith. Take hold of the eternal life to which you were called and about which you made the good confession in the presence of many witnesses. 1 Timothy 6:12 ESV

ὁμολογία – homologia
profession:
subjectively: whom we profess to be ours
objectively: profession [confession] i.e. what one professes [confesses]

Profession :
PROFES'SION, noun [Latin professio.]
1. Open declaration; public avowal or acknowledgment of one's sentiments or belief; as professions of friendship or sincerity; a profession of faith or religion.
The professions of princes, when a crown is the bait, are a slender security.
The Indians quickly perceive the coincidence or the contradiction between professions and conduct, and their confidence or distrust follows of course.
2. The business which one professes to understand and to follow for subsistence; calling; vocation; employment; as the learned professions. We speak of the profession of a clergyman, of a lawyer, and of a physician or surgeon; the profession of lecturer on chimistry or mineralogy. But the word is not applied to an occupation merely mechanical.
3. The collective body of persons engaged in a calling. We speak of practices honorable or disgraceful to a profession
4. Among the Romanists, the entering into a religious order, by which a person offers himself to God by a vow of inviolable obedience, chastity and poverty.

Confession:
CONFES'SION, noun
1. The acknowledgment of a crime, fault or something to one's disadvantage; open declaration of guilt, failure, debt, accusation, etc.
With the mouth confession is made to salvation. Romans 10:10.
2. Avowal; the act of acknowledging; profession.
Who before Pontius Pilate witnessed a good confession 1 Timothy 6:13.
3. The act of disclosing sins or faults to a priest; the disburdening of the conscience privately to a confessor; sometimes called auricular confession
4. A formulary in which the articles of faith are comprised; a creed to be assented to or signed, as a preliminary to admission into a church.
5. The acknowledgment of a debt by a debtor before a justice of the peace, etc., on which judgment is entered and execution issued.