This will partly depend on how you're planning on using those blankets, how frequently you're washing clothes, and your budget.
During the newborn stage, you may find that you're doing laundry almost daily, so you might not need as many blankets.
Yet, most moms find that having around 10 to 12 blankets is ideal to avoid running out. This may hold especially true if you're swaddling and want to use a fresh blanket every time, or if your baby has frequent diaper blowouts.