Not everyone who has used this name is making a religious statement.
The first time I ever came across a child named
Trinity was on an airplane flight back around 1990 when I sat next to a woman who had a toddler daughter named
Trinity. She told me the name had been chosen because her husband was a professional jockey and one of the horses he had ridden had been called
Trinity! And when I asked her about the religious meaning she said "We're Mormons and don't believe in the
Trinity."
I think the name has also been used as a transfer from the name of several rivers in the western United States and so is sometimes considered a "cowboy" name without any reference to the original religious meaning.
Though personally I would never use it because as a
Christian who does accept the
Trinity it seems to me it's the same thing as naming a child God.