[Liz]

..... last names of the mother and the sons—----not the same.....

That's b/c they use several identities (they vote and collect piles of US govt money under various names).

She also knew she was in big trouble and falsified police reports w/ a fake name ----- she did not want to give one of her gravy-train identities for fear of losing money.

[Vinnie]

That's b/c they use several identities

Heck, they have two legal identities before they start schmoozing the law.

Ricardo Gonzales y Suarez.
So he is Ricardo Gonzales or Ricardo Suarez, legally.