You say you have a 'company' hosting your podcast. Please tell me it's not Anchor, or one which has submitted your podcast under their Apple ID rather than yours. If this is the case then it's entirely up to them whether they allow you to move to a different feed URL. If you have full control over the feed, then you can change the Store and subscribers seamlessly to another feed and retain your reviews and stats. However you have to do this under the same Apple ID it was submitted with.
The methods of changing to a new feed are described here: http://wilmut.uk/move (section: 'Changing your feed URL').
However if you can't get access to the feed or to Podcasts Connect, and the company hosting it won't transfer the podcast to a new feed for you, then you will have to start again from scratch. You will lose your subscribers, reviews and stats (except that you could add an episode in the current feed announcing the change to a new feed and asking subscribers to re-subscribe). Ideally you would want the current one removed from the Store - that would be up to the company currently hosting it if you can't access Podcasts Connect for it. If it isn't removed you will definitely have to choose a different name for the podcast, and possibly even if it is.
