Using the same name for the drive shouldn't be necessary, though it wouldn't hurt. When you open a Team Project on a new computer, the software will scan all of your mounted drives to see if it can find a file with the same name in the same relative location. For example, if one editor imports the file /Volumes/MyDrive/ProjectA/Media/Shots/Shot1/Something.mp4 then shares, then when that Team Project is opened on another machine that doesn't have the file in that location, the software will automatically check each mounted volume to see if it has the file /ProjectA/Media/Shots/Shot1/Something.mp4. If it finds such a file, it will use it. (If it finds multiple matches it will use some rules to figure out which one is most likely to be the original file). This works between Mac and Windows, too.
If the directory structures aren't the same, you can use the Media Management dialog on each workstation to tell the software where to look (Edit->Team Project->Media Management). For example, you can create a media mapping that says media from /ProjectA/Media is located in /MyStuff/Projects/ProjectA/Media on this machine.
Does that help?