My daughter has this so I bought her to eye doctors. In most cases, these
are benign, so no worries.
There could be a lot of reasons for infant to have this, it could be racial
melanosis, melanosis oculi, a nerve loop, congenital nevus or something else
. Note that in case of melanosis oculi and congenital nevus, yearly
monitoring is recommended. Still, the doctors won't be too concerned about
them.
The only bad thing is that none of them will fade with time. Some will grow
slowly until adulthood. There's a cosmetic concern in such case. Still,
There's nothing we can do about theses spots.