You can use geom_text() or geom_label() to add text to points. You will probably want to subset your data set to just a few points and do something like
+ geom_text(mapping = aes(x = spin_rate, y = sw_strike_pc, label = player_name), data = ReducedData)
There are parameters like vjust, hjust, nudge_x and nudge_y to tweak the text position relative to the points.
If you make a reproducible example, my suggestions would be less likely to have errors because I could test them.