They called themselves Christians but that isn't what you've stated. I don't believe they called themselves "Catholic Church fathers".
"They called themselves...?" In your opinion, were they or weren't they?
...I don't believe they called themselves "Catholic Church fathers."
The differentiation "Catholic" was not necessary until the proud heresies of the 16th century; but the Catholic Church is as it was from Pope Peter I until now.
Did they call themselves Christians? I’m asking that as someone who isn’t sure how they referred to themselves as His followers.