Eros in not purely the God of erotic love. Eros is actually the god of love in general. He is actually one of the oldest of Gods in Greek mythology (not age wise in the myths, just first worshiped and 'created' by Greeks). He was originally a handsome young man, and in later myths transitioned to a cherub. He always carried arrows, two sets: one tipped in gold and ended with dove feathers, which caused love, and one lead tipped with owl feathers, which caused aversion. He traveled with his mother, Aphrodite, and did her bidding in causing mortals and gods to fall in (or out) of love.
I think erotic love is something nice. But I wouldn't use the name anyway. Although it's an old and kind of time-honored name, it would be associated with nasty things, like porn.
I always pronunced this name "AER-os". It sounds very pretty, but I wouldn't call my kid Eros. It comes from a Greek word meaning "sexual love". I always thought Eros was a girl's name. Erato is the muse of erotic poetry.
The tale of Eros & Psyche is a well known Greek myth. It featured the God of Love falling in love himself- with a mortal woman his mother (Aphrodite) despised. However, despite the many hardships and mishaps that came with the romance, Love (Eros) & Soul (Psyche) were forever joined.
Despite falling in love with Psyche (which does not really translate as soul, but more like "life" or "to breathe") the divide between Eros and Aphrodite on their shared domain is thus:
Aphrodite: Love between men and women. Eros: Love between men.
But, one must consider that there was no heterosexuality or homosexuality to the Greeks. It all fell under "love."