When we write the neutralization reaction.....
#NaOH(aq) + HCl(aq) rarr NaCl(aq) + H_2O(l)#
...bond formation has clearly occurred for the formation of water, i.e. strong #O-H# bonds have been formed..... However, the metal and non-metal ions remain in solution as their aquated ions; we write #NaCl(aq)#, what we really mean is the aquated sodium cation, which is possibly #[Na{(OH)_2}_6]^+#, a coordination complex if you like where the water molecule is the donor....and a similar aquated chloride complex.
And when we get the reactants into solution, #[Na{(OH)_2}_6]^+#, remains substantially unchanged during the reaction; it is a SPECTATOR that cheers on the bond-making reaction between the ACTIVE hydroxide and protium ions.....
#H_3O^+ + HO^(-) rarr 2H_2O(l)#
If you have further queries fire away, because this is a very important formalism to appreciate.