For noise nuisance, West Berkshire doesn’t say that reports can be made anonymously on the noise page itself. The published noise guidance points you to the Public Protection Partnership website for more information, and the council’s general noise nuisance complaint page is here.
If you want to report a different kind of issue anonymously, West Berkshire’s records do say some other complaint types can be anonymous, but for noise I can’t confirm that from the available council information.