How to travel to EU when passport name different than other documents?

travel
CAROQUIRO asked:

HELP!!!
I have a Colombian passport and need to travel to the EU. My passport has my before family last name but I got married and took my husband’s last name. Now all my documents including the green card has my new last name.
The tickets were issued with my new last name (though the company I work for) but they do not match the passport names. Colombia doesn’t change the passport names.
Will I have a problem to apply for the Schengen visa or travel to the EU?

Any answers much apreciated!!!
Thanks!