The problem with two browns is, it doesn't distinguish between the two sides of the power supply, or the non-isolated supply.
Colour coding is somewhat arbitrary. It depends on the wiring standards. For the purposes of this post, I assume you're using the European colour coding system: blue = neutral, earth = green & yellow, phases 1 to 3 = brown, black, grey.
Unless there's any need to distinguish it from the non-isolated mains supply, brown and blue should be fine, as what you have is an IT earthing sytem.
https://blog.phoenixcontact.com/marketing-sea/2019/01/grounding-system-types-according-to-ieee-standard/If you need to distinguish it from the non-isolated mains supply and it's a purely single phase system, you could pick two other colours from the three phase system such as grey and black, that way it's easy to tell it's the isolated supply and you know which conductor is which.
The above should apply to other colour coding standards, unless it explicitly states what colours to use for an isolated supply.