Is it possible to have https with custom domain name in Public Object Storage ?
I have the same question.
Well.. yes… but
The "standard" way, you point to the right domain, like https://storage.gra.cloud.ovh.net or https://auth-.stroage.gra.cloud.ovh.net then you'll get the match against the wildcard certificate, and you can return the objects in a https:// webpage.
However, using https://docs.ovh.com/gb/en/storage/pcs/link-domain/#http-https to point the browsers to it: nope, it'll be http://"only" as browsers will throw errors.
It might be interesting to check the us of OVH's SSL fronting, but I don't yet needed that.
What I can say: using CloudFlare (I believe I documented it elsewhere) where you make the CNAME (as described above) the proxied by CloudFlare, and then ALSO add the TXT record as per the above, did gave me the abilities to have custom domains fronting OVH object store inside https:// pages 
Other than those: use something like caddy/nginx/etc. to front the object store could always put it in several VPS for availability 