A drive letter CAN NOT be permanately attached to a drive when they are transferred to other computers. In each computer you will have to change the drive letter to that of your choosing .

each windows operating system assigns the drive letter accordingly to the order of recognition....in such, if you have computer 'A' with a drive configuration of
C.....system
D.....CDrom
E.....DVD
F.....new drive (USB)
G....new drive (USB)
note that any memory card slots for cameras will also show up as individual drives in order as well.

and computer 'B' with the following configuration
C......system
D......DVD/CDrom

If you remove 'F' from computer A and install it to computer 'B' then then windows will assign it the 'E' designation as it would be the next progression.

This is what you are experiencing.
SquirrelMoose shows you how to change the designations in the link above and you will have to do this every time there is a computer change.
Sometimes this is confusing as you will have to be swapping drive letters all the time.
SUGGESTION
With situations like this...I suggest that you (re)name the drives as this will help in identifying them in your situation and the names WILL carry over to each computer. The names are for identification only and as such have nothing to do with pathes to the drives.

to change the name of a drive:
R.clk "my computer" >explore>R. clk the drive you want to change the name on > properties.

The drive's name is highlighted (next to the icon) just change this to what you wish to call it and select the apply tab to instantly change it. Now no matter what computer you insert the drive on it will be identified as to that name.

The other part of this suggestion is to permanately re-assign the drive letters to your permanately installed optic drives on all your computers. (and any permanately mounted memory slots ) I use the X,Y.Z letters for my optics drives so that any installed harddrives will automatically be installed as the first lower end of the alphabet

example
computer configuration:
C......system
Z......DVD
Y......CD
X.....memory slot
W....memory slot
notice that the assigned drive letters will always show up as shown. For any add on drives they will be assigned the
D', E,F letters and I don't have to constantly change the optics drive letters.

Hope this helps!