Three different computers, running three OSs; Vista Home Premium, XP Pro,
and Win7 Pro 64-bit.

My Vista laptop used to be connected to a certain Canon printer, and its
name in Control Panel/Printers is "Canon iP6700D" and when I click on
Properties, and the Share tab, that is also the spelling of the "Share
name".

If I am trying to network to that Canon printer, which is now hard-cabled to
my Win7 computer, should I delete that printer reference on the Vista
laptop, using Control Panel? I wonder if having that entry in the Vista
system is somehow a problem in my efforts to nework it.

The Win7 computer is hard-cabled to that Canon printer. In Control panel,
the name under the icon for that printer is Canon Inkjet iP6700D, and in the
Sharing tab under printer properties the Share name is exactly the same.

I did manage to setup network access to that printer on the XP computer, by
setting up the port using the computername of the Win7 computer. BTW, this
same printer used to be hard-cabled to this XP, and there was already an
icon for the printer before I bought the new computer. In Control panel, the
name associated with the printer icon is "Canon iP6700D" but the Share name,
in the properties/sharing tab, is "CanoniP" Regardless of this difference,
I can print to the Canon just fine.

Is it known for certain that it is important for all names, including the
Share names, to be the same on all three computers? If it is, how would I
go about making all the names the same? Would renaming in Control panel
screw up something?

I think that I should know the unequivocal facts about printernames and
Share names before I make any more frustrating attempts to network the
printer to my Vistap laptop. If and when I get that done, I will start on
networking the HP Laser!