No. Ting can typically monitor the entire electrical network of your home from one outlet. There is no need to move Ting once it has been installed unless instructed to do so by the Ting Support Team, or if your Wi-Fi signal proves to be unreliable in that location.
If your house has more than one main breaker panel, you may require more than one Ting. You can check here to see if you might need more than one Ting for your home.