Unless you have a good reason not to, your edit form fields should be pre-populated with values from the database - so if first name was filled in by the user before, the field should have the value in it. This way, if a field is blank then it was always blank and you can save it as such without a problem. You can use default values or auto-binding to achieve this.
That being said, you can a) set fields to be mandatory, using the ‘… should not be empty’ flag; b) set conditions to disable the Update button unless all/certain fields are populated; c) use the Only when condition in your workflow to allow/disallow updates. It really depends on how exactly you have set things up.