Yes, it's possible to do it and there are no repercussions - apart from the obvious fact any outside URL to the original site will not work anymore. We do charge a fee for this operation.
Please log in to https://moodlecloud.com/app/en/portal/ and open a request from the "Support tab" if you would like to go ahead with this.
Am I able to do this manually? Now, if I were to do it through you guys, will I need to do a backup and restore somehow after I get my new url?
Sorry, this is a task that has to be performed rewriting some links), which has to be done while your site is inactive. There is a short maintenance window (a few minutes) where your site is offline while this is happening.-side as it requires some operations directly in the (like
No other operation is required from your side (no backup/restore).