I see that pinging my domain returns "n bytes from xyz.members.linode.com", which gives away too much for my taste. On the other hand, I've pinged plenty of domains that just return "something.domain.com". Is it possible to configure a VPS to have this behavior? If so, how?
If you register domain.com, whoever looks after the reverse mapping for your VPS' IP-address in DNS should be able to make the reverse DNS lookups for that IP-address resolve to something.domain.com.
Of course, people will probably still be able to work out that the IP-address of your VPS comes from a block of IP-addresses allocated to linode.com.
You can configure the PTR record for linode in their control panel.
In the "Remote Access" tab, look for a link labelled "Reverse DNS" in the "Public IPs" section.
The address would be https://manager.linode.com/linodes/rdns/[your linode name].