Does Jotform have the ability to send notifications when a form has been completed and submitted to my inbox?

Thanks for reaching out here!

Yes, it is possible to send notifications to the configured emails as well as send autoresponse emails to the form submitter.

Also, you may be able to receive mobile notifications:

https://www.jotform.com/help/574-how-to-customize-notifications-in-jotform-mobile-forms/

Should you have any further queries, please let us know.

Thanks.