First of all, you can see this link in your Dashboard, right under your Account ID (it's blue). When not customized, it looks something like this:
So, the "m.me" link is defined by your Facebook Page link. To change it, go to your Facebook Page and click "About" on the left panel, then press "Create Page @username" to set up your new page link. You'll just have to reconnect your Page in ManyChat using "+" button to apply changes to your account. That's it - you're awesome.
Hope this helps!