In all cases the domains will still show in the logs, so that will not work unless you disable it also on the client side.
Also, we can’t really encrypt it, so we can only hash it for example. Which in the case of domains also isn’t very useful. Because even if you hash it with sha512, these strings are probably easy to generate rainbow tables for. While we could use some user defined pre or postfix, it will only generate extra overhead, and you should also disable logging.
So, if you really do not want your domains on the filesystem.
Disable icon downloading on both Vaultwarden and every client app you use. Disable logging for both Vaultwarden and your reverse proxy.
And!! Don’t forget if people can see the files, the probably can also open them, in which case they see the logo which tells enough.