If your risk is being seen by your employer, then the cost of an intermediary shouldn't be too high. Family trust? You're paying somebody for the incorporation of some entity, to be the holding entity, come what may (ie, nothing is free)
Domain names: easy. Just chose the 'hide registrant' options in the domain registrar.
The hiding wont stop you falling afoul of IPR contractual obligations. If you signed the form, your work may belong to your employer come what may. non-compete clauses too. Deliberately trying to avoid this, by "hiding" is not sensible. It will only increase your burdens in law if it goes there. (it goes to intent)
But don’t you have an employment agreement with your employer? An IP assignment? A non-compete? A duty of loyalty? A duty not to usurp corporate opportunities? And I don’t mean a vaguely moral sense of things you should do to be a “team player,” but actual legal duties you owe to your employer.
Talk to a lawyer before you do anything like this. Make sure you’re not offsides.