I have some domains in OVH, they do not charge for privacy.
Generally you can check out https://tld-list.com/tld/com for the list of providers which offer free whois privacy for a given domain.
Be careful with OVH, they put your details in Admin-C/Tech-C, same effect as not using their service at all. At least that was my experience a few months back, I then switched to namecheap to avoid that.