Use the adverb variably for things done in an inconsistent or ever-changing way. Your family's beloved pet may be variably referred to as "Mr. Fluffers," "Fluffernutter," "Fluffy," and "that annoying feline."
When something changes or fluctuates, it's variable. So when things change in this way, they happen variably. The wind blowing variably on a stormy day may make it hard to steer a sailboat, and you might be angry that the rules in your school are enforced variably rather than applied consistently. The Latin root of this adverb means "change."