How to set DHCP / computer name on iMac

is computer name and host name the same thing?  I didnt understand the instructions on the page.  Pls explain.

They are one and the same.  use the post guiding you through the use of the system preferences to set the sharing computer name.
I think by default there is no hostname which means that when you view the DHCP server/listing you see a blank or * and then an Ethernet Address (MAC Address) in the form of xx:xx:xx:xx:xx:xx.

Yes, they are!

if they are one and the same, then the existing computer name "Dan's iMac" is not showing in the router.

Dan's iMac might not be what the hostname is set to.

If you open a terminal and run the hostname command, it will likely be empty of *.
Follow the system preferences and see.
Dan's iMac is that the label on the Hard Drive?

Sorry I'm new to macs, what do you mean by opening a "terminal"?

http://www.mac512.com/osx/systempref.htm

Go through system preferences and set the hostname within network identity.

Ed,
I think your suggestion is the right one as I just found it whilst playing around before looking at your thread again, but having added a client ID and refreshing the router page again, the client id still does not show on the router.

Did you reboot the system in between?  You can try the release/renew.?
The ID is set when the IP is acquired. Subsequnet are just renewal notices saying I have IP X is it ok for me to keep it?

Go back to the preferences and see if the id is still set. You have to click ok and when that window goes away, click Apply on the main network preferences page. It is also possible that your router does not pick up the id from mac. Just guessing on that though.

yes, done all that but still doesnt show in the router.

Try deleting the router entry for the mac address/IP and then get the Mac request/renew the IP.

how do you delete the router entry, I dont think its possible.  Only way is to restart the router I believe so that existing data stats are wiped.

Also what happens if for example I have the ethernet cable from the router going into a Vonage (voice over IP telephone) device and that vonage device has another ethernet output which then links to a different computer (so that the computer can daisey wheel of the back of the Vonage).  Does this appear as only one mac address i.e. Vonage's in the main router settings or will I see 2 mac addresses?  

I know I can obviously check myself, but I've never seen a DHCP name for the vonage device and furthermore there are 2 blank clients showing on the router page.  

I think the vonage connection is a pass through.
Since your router allocates the IPs, there should be a place that lists all the reserved/allocated IPs and where you can delete the entry.

Which router are you dealing with?

You can use the MAC address at http://www.coffer.com/mac_find/ to determine to which manufacturer this device/system belongs.

I'm using a belkin router.  What do you mean by pass through; that the IP address of the computer connected to the vonage device is not being shown because it is going bia the vonage box?

Possibly Yes, It depends on the functionality of the vonage box which I think is acting as a router or it just forwards the requests your computer makes.
.
Presumably this is what your setup looks like
Internet <=> belkin <=> Vonage <=> Mac
Though I am uncertain why you do not have the following setup

                              Vonage Box
                               /
Internet <=> belkin
                               \
                              Mac

It's like this.

                                  PC 2
                                 /
                Vonage Box
                               /
Internet <=> belkin ------- PC 1
                               \
                              Mac

And the belkin router is not reflecting the hostname for the Mac after you made the changes?

It does, intermittently.  

What is the length of the IP lease?
Does the intermittently have to do with the belkin being rebooted?
i.e. your lease time is 7 days, and in the event the belkin is rebooted within this seven days windows, it reflects that something is using x.x.x.x but not reflecting the name?

This can be explained by the mechanism that the Mac already has an IP leased to it so it does not send a request for an IP it either simply using it and the belkin reflects the IP/Mac based on usage, or after the lease expires, the Mac merely issues a DHCP renew request which the belkin approves, but does not retain the hostname originally provided to get the IP.
This can be confirmed:
1) reboot the belkin and the Mac. IP assigned, hostname reflected?
2) the belkin works continously as is the Mac, the lease expires and the Mac renews the IP but the belkin does not reflect the hostname?
3) rebot the belikin, while the mac remains up, does the client list reflect the IP but not the hostname?

this is getting a little more technical than I am used to.  what do you mean by lease time?

One of the options within DHCP is the duration for which the Allocated IP is assigned.
i.e. you turn computer A on. It requests an IP from the DHCP server and gets IPA which includes the period of time computer A has "rights" (lease time) for the IP.  when the lease expires, computer A will go through the process of renewing the IP it has, if the DHCP server already allocated the IP, the request to renew will be rejected and computer A will go through the process of obtaining a new IP.

http://www.tcpipguide.com/free/t_DHCPLeaseLifeCycleOverviewAllocationReallocationRe.htm

The issue could be that the belkin flushed the host/IP when the Lease expires, such that when the Mac attempts to renew which it might, the belkin only has the IP that is being renewed and since it flushed the hostname/IP from the original request, all that remains is the MAC Address and the IP the mac has, the hostname is not there.

sorry didnt have time to fully test this, but will close the q anyway.  thx.