Please fill out the following sections to the best of your ability, it will help us investigate bugs if we have this information at the outset. Screenshots are especially helpful, so please provide those if you can.
Platform (Android, iOS, Website): Website
Browser, if a website issue (Firefox, Chrome, etc) : Firefox
URLs (aka web addresses) of any relevant observations or pages: https://inaturalist.ala.org.au/taxa/537414-Zieria-collina
Screenshots of what you are seeing (instructions for taking a screenshot on computers and mobile devices: https://www.take-a-screenshot.org/):
Re-ordered common name priority:
Back at taxon page:

Description of problem (please provide a set of steps we can use to replicate the issue, and make as many as you need.):
First, I added a common name (hill Zieria)
Step 1: Click manage names
Step 2: Drag common name (hill Zieria) to top
Step 3: Click save changes
Step 4: Review taxon page, common name has not changed
Step 5: That the order has not been changed can be confirmed by clicking Manage Names again
Step 6: Additional check that common name priority has not changed can be seen by clicking Curation/History (https://inaturalist.ala.org.au/taxa/537414/history)