To deny His name

What does the Lord mean when he says “those who deny my name”? Does it just mean abandoning the church or does it mean denying Christ himself?

To say “I believe in God…” or even “I believe in Christ himself but I do not believe that this temporal organization represents Him now (if it ever did),” is quite different than “I reject the existence or supremacy of God and will fight against those who testify in favor of such a being.”