I have a DFA A, I minimize A and the minimized DFA obtained is M. My question is if in general A and M are isomorphic?
No. If the result of minimizing was always isomorphic to the thing you started with, minimization would do nothing!
For a concrete example, consider any automaton with more than one state, which has every state accepting. This automaton accepts $\Sigma^*$ and is not isomorphic to the minimal automaton for that language, which has just one state.