First check how much iCloud storage you have left by going to Settings > [name on top]. Then go down to iCloud Backup, choose the device that says "This iPhone". You will see under Next Backup Size, how much storage will be needed for the next backup. It may say Loading for a short period of time. If the next backup requires too much storage space, you can turn off what you do not want stored there.
Also since it is a new phone, you most likely still have a backup from your old phone. This will be at Settings > [name on top] > iCloud Backup, and you can tap on the old device to remove that backup. This will free up some space so the new phone will be able to perform a complete backup.