Hello @Hejms,
Okay it’s fine that you can’t remove it, but is there a way to hide it with CSS then? 
This is not the proper way and hence we do not advise to do the same but if you want to hide the Wall Posts
album anyhow then you can override the rtMedia album template under your child theme and add related custom code.
Here, is the sample code you can use into your custom template - https://gist.github.com/pranali333/817bd38dccf4915d09a0aad4e72b689d
It will add a class hide
when it finds the Wall Posts
album.
Note: Media uploaded without selecting the personal album will be stored to Wall Posts
and you hid it so it won’t get displayed under profile.
Here is the document which can help you with template overriding - https://rtmedia.io/docs/developers/themes/templating-system/
If it isn’t possible to hide it, can you then rename it and make it non-global?
Yes, it is possible to rename the default album. We have an add-on available which allows create and modify multiple default albums for rtMedia uploads. It is having admin settings using which you can easily update existing default album names.
Please visit the product page here - https://rtmedia.io/products/rtmedia-default-albums/
Here is the documentation link - https://rtmedia.io/docs/addons/default-albums/
I hope it helps you.
Thank you.