The wedding itself is a memory that she shares with us and her father/family so we know that she’s married now because we saw that moment, also she already called Max her husband. The reason of why she said “Parker” is simple and rather metaphoric: Katims said that she ended the journal with “Liz Parker” because it’s Liz Parker that started it so it was very fitting that Liz Parker started and ended the show, basically. “Liz Evans” is a new chapter of her life (perhaps a new journal could be started like that) and in that moment she was saying good bye to the old Liz, the one who wrote that journal ;)
At the same time I always thought that she said “Liz Parker” because she was talking with her family.. in a way she was telling her father that even though she’s married now and far away she still is their daughter and she won’t forget them.
Most likely they aren’t using their real names anymore.
But it’s not the “Evans” that makes them husband and wife
*although I think that they used their real names when they married so that it was legal too… it could be the main reason of why they chose a secluded place for the wedding and they left asap. Even if the FBI knows that they married this information won’t put them in danger.
“We won’t let go of each other’s hearts and overcome everything. Cause you are my everything to me”
This reminds me of Max & Liz^^