I wouldn't say I'm fake, I'm different versions of myself. I'm more polite or more friendly based on necessity but like, when I'm on a till and I tell someone to have a nice day, I don't secretly wish they had an awful day, I'm just fitting myself into the role I have to take. Sometimes when I smile at strangers it's genuine, especially because I've got a bit of social anxiety and I naturally smile when I'm uncomfortable. I wouldn't call that fake, if they think I'm just being friendly then that's them misinterpreting my own signals. Not my fault.
Sometimes I'm a bit serious and I have to tell myself to chill or lighten up but that doesn't make me fake either. It just means I'm aware of how others are perceiving me and I want them to see a different side of myself. No one talks to their parents the same way they do their friends but that doesn't mean you can't still be yourself in both situations.