I'm thinking of signing up but I have one concern. Can the whois of a linode IP be changed to show my business name instead of linode's?

Thanks

IINM, reverse DNS, yes. whois, no. Pretty sure you need a subnet delegation to get that and you're not going to get that on a single linode.

It's worth noting that the same will be true of any host; they own the IP, so they show up for the WHOIS. But even if you could change it, someone could just do a traceroute to find out where you host.