Some others say this is entirely your own choice and you needn't tell anyone.
I disagree. This is not like playing sport or being part of the university drama troupe. There is serious time and head-space demand accompanying this activity. A supervisor has a right to know this, I think, as there is a risk of distraction from your own work. There is also a risk of disaffection among others in the research group if they sense a lack of commitment to the work in hand.
I don't think any decent supervisor will impede you if there's no bad impact on your work - in which case you stand to even benefit mentally/socially from it. But be aware that philosophy is not about ideas alone: it's a strict mental discipline and you have to clearly and rationally explore these ideas. It's not for nothing that Phil graduates quickly master other (and very competitive) professions like law, accountancy, business management, etc. Having met one or two Phils in transfer courses to software eng, I was always stunned at the strength of their logical faculty.
I'd be more worried about attitudes of other PhD students in your group. Maybe you could ask your supervisor to keep this between yourselves but not deny it if someone twigs.
Finally, if it needs to be said, don't wall out too much of your spare time so that there's no time to relax and try and keep a normal social life for someone of your age - i.e. unstructured and mutually discretionary engagement between people. We all need to engage with someone on a purely human level. While this may not enhance our rational mind in any way, it will enlighten our appreciation of the human context of our work and this in turn feeds into our motivation to work creatively and pleasure in such achievement. Studentship grant allowing, of course!