It seems that the logic of Conditional fields is based on the tag of a field option rather than, say, the field option's ID. As such, in order to make a change to a ticket field's tags, I have to totally remove the condition, make the change, then re-add the condition back. Not only is that tedious and error-prone, but it means that if someone is actively using the form during the period the conditions are removed, they could have a strange list of form fields.
In my case, I set a field option as "Deployments" with the tag "deployments" that has conditional rules set up when it's selected. But then the name changed slightly to "My Assessments". I can change the field option name, but the associated tag wouldn't make sense with that option, so I'd want to change that too. The conditions related to it haven't changed, but if I want to change the field option's tag, I have no choice but to remove the condition.