DHCP and DNS on a home network

Let's say I have a home network containing a server that acts as the resident gateway and serves dhcp and dns requests. Laptop A is frequently connected and disconnected from the network as it is used as a travel computer. Is there a secure way to make sure that whenever laptop A is connected to the home network it is always reachable at the same hostname but is configured to acquire its IP information dynamically through dhcp, as it would have to do if it were connected to any other network anywhere else?

I am new to dns, but it seems that there is a fair amount of manual configuration required, which is odd, because dns was developed so that lazy people didn't have to memorize squillions of cryptic internet addresses. Hell, dhcp is yet another tool developed because of the laziness of sysadmins. It seems like there should be a way to let their laziness work together. I tried looking up some stuff on Dynamic DNS, but it seems that that's something completely different. Any light shed on this matter would be greatly appreciated.

Please mention the Operating System and version of every computer involved in this network and make it clear which computer is running as a DHCP server. If this is not unix/Linux please make it emphatically clear what Operating System is installed.

Must assume that this is a standalone network with no Internet connection whatsoever because it would be weird for a Home Network to not use the Internet Router as a DHCP server. Unless you have paid for an external Fixed IP Address?

Anyway I can't see what your problem is. Providing that the laptop has a hostname set, this will be associated with the DHCP IP address. This assumes that your DNS server is working correctly.

At the moment this is mostly a hypothetical situation. The laptop in question is running Ubuntu 12.04, the server does not exist yet but will probably run FreeBSD. The other hosts on the network are running FreeBSD 9.0. The internet connection is through a cable modem, so dhcp of some sort is required on the home end.
Is this basically a case of rtfm for DNS and hostname configuration?

My advice. Use the Cable Modem for DHCP IP address allocation. Just stopping it doing that job would be a major task in its own right with a Home Network setup. The same applies to DNS.

I am assuming that you are not running a Corporate Network (as distinct from a Home Network) and have not paid your ISP for a Fixed IP Address and control over the Cable Modem.