Hello and welcome to Apple Support Communities lillafrombudapest,
It looks like you're experiencing issues adding your Philips Hue smart lighting to HomeKit. I know what an inconvenience it can be when devices don't sync together like you expect them to. I'm happy to help you with a solution for this.
Some accessories have extra hardware requirements in order for them to work with HomeKit, and Phipps Hue is one of them. It require a Philips bridge device as seen here: Philips Hue Bridge. Do you already have a bridge? If so, you'll need to set up your bridge in the Philips Hue app first, which is another requirement for for this device. You can view the steps on setting up the bridge here: Philips Hue: How to pair your bridge to Siri. Once your bridge is paired to your iPhone, it should be automatically added to the Home app as well. For more details about HomeKit and controlling devices uses the Home app, take a look at this support article: Use the Home app on your iPhone, iPad, and iPod touch.
Let me know if you're still experiencing problems getting everything set up, as well as if you're getting any errors when doing so.