flash drive recognition by different computers is not the same

I may know how to resolve this issue, but would like to have confirmation before making any changes. This represents a learning experience for me.

I use two flash drives on a regular basis. One is reserved for school files and assignments. The other is used at home. I have given both flash drives unique names, but have not assigned drive letters to either one. In an attempt to troubleshoot, I have tested both flash drives on all the machines I use on a routine basis.

The machines are:

• two HP desktops running Windows 7 Professional at school
• Dell desktop running XP at home
• Lenovo laptop running Windows 7 Home Premium (specs listed in my system specs in this forum)

Here is what I have experienced:
All but the Lenovo recognize the flash drives by the names I have given them. The Lenovo does not recognize them by name. In computer, the drives are listed as "Removable disk G:". In safely remove, they are listed by brand name and the drive designation listed in computer.

This is why I believe I experience this behavior:
All but the Lenovo have only one USB port available for my to use for the flash drives; therefore, those machines do not randomly assign a drive letter to the flash drives. The Lenovo has 4 USB ports available, and they are used by several USB devices. Windows will assign a drive letter based upon what was last used. It is complicated by using multiple USB devices in the several USB ports. Is my understanding correct so far?

If my logic is good so far:
(I am trying to connect some dots here.) My external drive for backups has been assigned as Z: drive and has a unique name. It is always recognized properly. I am thinking that if I assign drive designations of X: and Y: to the flash drives, the drives will be recognized by name on the Lenovo. Is this correct?

Thanks for your help.

drpepper