Hello chrisf-1
The option "Assign or Change Drive Letter" does not show up because the disk doesn't have a file system (it's not formatted yet). Follow og's procedure again but instead of the "Assign or Change Drive Letter" option, look for "New Partition..." and follow this procedure. The wizard is pretty straight-forward but just in-case:
1) Click Next
2) Select "Primary Partition"
3) The next window gives you the option to make multiple partitions so if you wanted to keep videos, documents, and pictures separated logically instead of through folders you could do so, but for the sake of consistency let it be and just click Next.
4) This is where you assign the drive letter. Windows automatically gives you the next letter in line, so just click next.
5) Make sure the "Format this partition with the following settings" circle is selected.
a. The first 2 input boxes should be set to [NTFS] and [default]
b. Volume label is whatever you wanna call you external drive, for example My Recovery Files.
c. Last is the "Perform a quick format" and "Enable file and folder compression" selection boxes. The first one should be unchecked only if there was data previously on it, but if this is a brand-spankin-new drive. Check the box and the second one I would recommend selecting IF and ONLY if you're using this external drive for backup files because then you can stuff more on it.
6) Before Windows does anything, you can review what you have selected to be applied to your external drive. Make sure Windows is gonna do a quick format. If you're going to do a full format...STOP. You did say this is a 1TB drive correct? While I'm not sure why it wouldn't already be partitioned but DO NOT click next just yet. 1,000 GB will take a looooooooong time to format. So...I would HIGHLY recommend doing this procedure in the evening so the drive formats overnight and even through your day of work. So make sure Windows will "Perform a quick format" and the click finish.
Now anytime you connect you're external drive to your machine, it should not require you to go back into "Disk Management" to assign it a drive letter. That really only occurs with flash drives, Lexar in particular.
Hope this works out for you.