Alias / tsuushoumei – Is there any way it could get cancelled?

I saw many threads about registering or using an alias, and I recently registered mine. But, before I go and use the alias to enter into contracts, etc. I am wondering if there is any risk of having it cancelled against your will? For example…

1. Each municipality seems to have their own rules on issuing the alias. If I move to a new city, and I already have an alias, is there a national law that they must let me keep it? Or is it up to their discretion?
2. Divorce! When I married, I didn't change my name, but my alias uses the last name of my (Japanese) spouse. If we divorce, can I keep the alias? Or again, is it perhaps up to each municipality?

I imagine that once the alias is on My Number card, drivers license, and various contracts (utilities, banks, etc.) then you can probably register it in almost any city, divorced or not, but would appreciate if anyone has experience on this or knows the rules.