The subject of a one-on-one conversation can not be changed. The subject of a group conversation can be changed by the owner and everyone with the propper rights.
In the web interface you can do this by opening the relevant conversation and going to ‘More’. Then click ‘Change subject’.
On your mobile device, you can change the subject by opening the group chat and opening the menu in the top right corner. Choose ‘Chat options’. Change the subject and click ‘Save’.