Both are pronounced same, right? How can we distinguish?
In theory both are not pronounced the same but in practice they are. In theory you should pronounce
ę which has a different pronunciation to
e.
Chcę, you say it wihout ja and people will understand that it is you who wants something.
If a you are saying that he or she wants something you put
on or ona or ono before chce and then everyone knows that he or she or it wants something. You use ono for neutral nouns like dziecko etc.
By the way, why is your name Zoe? In English that is a girls name as far as I know.