When parents receive notifications from Seesaw, they don't see your name as teacher, instead they see the name of your class. So for example parents in Rhys class would see '2PERVo' as the label that identifies that post as a PE post, but they wouldn't see the PE teacher's name.
So parents with students in multiple classes (from G1 up) will know that posts some from different classes because of the label with the class name.
The problem is some class names are little ambiguous, especially for EAL parents, in the case of the class above, it (pervo) could even be seen as rude!
This is not a major issue, but if you would like your class name to appear differently, you can do this in Seesaw settings: Manage class > Class Settings > Class Name.
So, if you prefer you could change your class name to a less cryptic name that parents (and students) would find easier to understand, but avoid making these too long; eg I have changed '2PERvo' to '2RVo PE'.