We know that a depletion region of a PN junction is that region in which there is no free charge carrier i.e. electrons or holes but only contains Ions of positive and negative charge.
We know when we apply forward bias, then the dominant current flow from P to N direction and the contribution of diffusion current is more than drift current.
Diffusion is occurring across the PN junction and minority carriers are being injected from higher concentration region to lower concentration region.
During diffusion it is crossing the depletion region, and since diffusion current exist for the entire period of time we are applying forward biasing. That means for entire period of time diffusion activity is being carried on, and since for entire period diffusion activity is being carried on, THERE IS ALWAYS SOME CHARGE CARRIER EXISTING IN DEPLETION REGION.
Then why it is called a depletion region as the region of no free charge.