I wouldn't say it's impossible, but it is very hard. As Maurits implies, there's only one reverse mapping through PTR records from IP address to DNS name - this name can be considered a canonical name for the address. My employer's external address is nn-nn-nn-nn.dsl.isp.net.uk, where nn-nn-nn-nn is the IP address with '.' replaced by '-'.
There are currently at least four DNS names, which are mostly in completely unrelated domains, which point to that address. (It's actually the external address of a NAT firewall, which maps different services to different internal boxes).
The only way you can actually do it is to search DNS. That's hard, because many DNS servers do not permit a zone transfer - a dump of all records in the domain. In fact I think it's now quite rare to permit this as obviously it gives an attacker an entry point.