Short answer: You can't.
You can try a reverse lookup on the IP address, but that will only show you the address that has been specifically allocated in the reverse DNS to that IP address.
Remember, aliases might exist only as an entry on a single machine's hosts
file. They might also exist in a DNS server on the other side of the planet. However, if you're only interested in local DNS aliases, and your DNS servers allow zone transfers, then you can try listing every entry in every domain (eg. with host -l xyzzy.bigcorp.com
) and searching the results for the IP address in question.