Is it required a dedicated IP?

Hi,

I have a hosting and all my sites from this hosting have the same IP. I installed my multisite wordpress in this hosting, so the multisite also has the same IP. I know this IP is fixed to my hosting. I read the related questions in the forum plugin but I still have this doubt: Is it required to have a dedicated IP to the Domain Mapping plugin? Given that my multisite has a fixed IP, is it required?

Next month, I will use a dedicated hosting. Will I have to change something in the Domain Mapping plugin after install my multisite in the dedicated hosting?

Thanks.