Do I need an EULA for my unregistered demo?

Thanks @SonsOfKorhal,

Please, I think you replied in the case of a registered trademark game, right?. But what about an unregistered one? Simply made something with Unreal, and packaged/compiled it; wihout any legal formalities, nor registrations, nor patents, etc.

I was thinking replies would be somthing like these:

Do I need anything more before release, or can I directly upload my
game and distribute it as mentioned?

No, you can just publish it.

Do I need to add an EULA, into a text file (for example), accompanying
the game? Mandatorily?

No, as your game has no ‘official’ or
‘legal’ name, as it has not been
unregistered.

That would be right?

Thank you again!