While creating the Character we chose the Two Weapon Fighting as a fighting Style. Today we started the campaign and realized that we wanted Great Weapon Fighting (non native english speaker) and tried to change it in the Character settings. After some trial and error we managed to change it in the character settings but it didnt update on the character sheet.

You may need to go to the Character Builder, change the Fighting Style back to (unselected), reload the page, then change to Great Weapon Fighting, then view the character sheet.

 Also don't forget that every character has 'Two-Weapon Fighting' listed under 'Actions in Combat,' because every character can perform a bonus action attack if they use the right kind of weapon and the attack action, they just don't get the buff to it that the fighting style gives. To confirm which fighting style your character has, you want to check under 'Features & Traits.'

Thank you! After checking the "Features & Traits" it does show the correct fighting style. Much appreciated

Not a problem! The double use of the name trips up a lot of folks.