The -1 charge on nitrate (NO3) is not on any particular atom. Nevertheless, assigning formal unit charge ensures accurate net charge and electron count.
A Lewis structure equates each bond with two electrons. In nitrate, two of the nitrogen-oxygen bonds are single (bond order 1), the third has a double bond (bond order 2). Lewis diagrams are ill-equipped to convey non-integer bond order.
Multiple Lewis structures are meant to communicate an "averaged" bond and charge distribution. Nitrate is represented as three diagrams, each with the double bond---and formal charge---on different oxygen atoms.
Consider cyanate, (OCN) with -1 net charge. The more electronegative oxygen has greater electron density than nitrogen. Cyanate has a lopsided charge distribution, negative charge slanted towards oxygen. Resonance necessitates showing double-double and single-triple-bond drawings to convey (asymmetrical) cyanate bond characteristics.
Combined over all atoms, charge distribution on nitrate and cyanate adds to -1, in agreement with formal charge summation for each Lewis diagram.