iOS uses a unique name for different services including the Bluetooth name and your iPhone's name. To change Bluetooth name on iPhone 6s and other iPhone, iPad and iPod touch devices do as follows:
1. Open the Settings application
2. Go to the General settings
3. Hit the About option
4. Now, tap the Name and type a new name for your iPhone (This new name is also assigned to your iPhone's Bluetooth name)
5. From now on, this Bluetooth name is shown when searching your iPhone for Bluetooth connection.