voltage regulator

Can I use my ATmega328p with my phone charger without 5V voltage regulator?

Without more information on what you mean by "ATMega328p" (bare chip? standalone board? what?) and your "phone charger" - there isn't enough to give you a proper answer...

yes, standalone chip powered straight from my 5V phone charger.

"Probably." Apparently there is a lot of variation in the quality of "5v phone chargers."

If it is USB charger then yes.