DNS name and dynamic IP

[sinister]

I connect to a Solaris box via SSH over VPN from my home Windows XP Home 
box.

I started finding all these weird names in the wtmpx file on the Solaris 
box.  (It's a log file with a list of users, connect times, connecting 
IP/name, etc.)

Called IT support and he said it was something like the following.  (Pardon 
my obvious lack of knowledge of the subject.)  One name server has been 
setup so that on reverse lookup the names resolve statically as 
vpn-xxx-xxx-xxx-xxx.domain.xxx.  The other name server, the one the Solaris 
box queries, was setup to lookup the name based on technologies related to 
DDNS, DHCP, etc.  (Here's where my lack of knowledge is showing.)  Something 
like, when someone connects, their client can carry a name that their ISP 
passes on to the name server.  These names are supposed to be deleted when 
the connection closes, but if it's not closed gracefully, they might not be 
deleted for a few days.  He thought it likely that my home machine doesn't 
have such a name assigned to it, so when I connect there's nothing to 
overwrite the stale record there (if there is one) for that IP address. 
Then when the Solaris box tries reverse lookup, it's given the stale name.

(1) Can I stick a name on my Windows box (something like first.last at isp.net) 
so the stale records are overwritten?
(2) What's the name of this technology?  (I tried searching on DDNS, DHCP, 
BIND, etc, but didn't have enough knowledge to use keywords that would allow 
a google search to answer my question.)
(3) Is the support guy's explanation accurate?  Or is their name server not 
behaving according to specs?

TIA,

S