Windows Server Backup with Two External USB

Wrong. WSB uses GUID namings and the gipuid names of the HDD to identify the storage. You can try the following: with one USB HDD connected create a backp job to HDD1. Let it run on Mon, Wensd,Friday.
Then disconnect this drive and create a job to take backups to this HdD2 on Every second day. This should work when the right drive is there.
Or you get a copy of Paragon Hard Disk Manager 15 Server Basic and plan a backup job to external drive Emfor example. And it will take backups not depending on which drive is connected. Exactly what you wanted from Win Server Backup.

"one USB HDD connected create a backp job to HDD1. Let it run on Mon, Wensd,Friday." --> I get that.

"Then disconnect this drive and create a job to take backups to this HdD2 on " --> am I essentially creating a second backup job? So create a first backup job with HD1, say, at 9PM. Let it run for a week (M-F). Then on 2nd week, connect HD2 and create a new backup job that runs at 9:30PM?

@Larry,

  "did you "show all available disks" and check both of them? "--> Yes. when I connected them at the time of backup job setup, I remember seeing "xxx DISK_01" and "xxxDISK_02".
 So I thought I am all set and what I have to do is to change the USB HD once a week.
 I have done this on another server and it is working fine. But I don't know what has gone wrong.

I took the screenshots from two separate servers where I run Windows Server Backup.
As you can see, the working site has disk_01 and disk_03 listed under "Destination Usage" section whereas the problem server only shows disk_01.
So the question is to have Windows Server Backup program to remember/keep both disk names and detect them automatically when they are rotated.

Connect both of them again and see if one is visible in Explorer.  If so, with both connected run the wiz again.  It will wipe the visible one but not the hidden one, so if whatever is on the visible one is important it may be better to introduce a third drive.

Are all the drives on both servers the same exact make and model?  While this should not affect it, can't be sure.

Well, the working file server has Seagate (I believe) 2TB USB HDs powered by AC adapter. I use one USB cable and have a designated person to unplug and plug Ext. USB HDs every Monday.
On the failing file server, I bought USB cabled powered ext. USB HDs by WD and I left two USB cables/connectors plugged into the server and asked  a designated person to unplug WEEK1 from that cable and plug WEEK2 into 2nd cable.

I need to wait until Monday to go thru the whole backup creation process again.
On Monday, I will connect both USB HDs and pay more attention to "Destination" section to see if WSB shows both ext. HDs.

am I essentially creating a second backup job? So create a first backup job with HD1, say, at 9PM. Let it run for a week (M-F). Then on 2nd week, connect HD2 and create a new backup job that runs at 9:30PM?

yes, exactly.

@noxcho
I prefer to create one backup job with two ext. usb HDs as destination.

On the second server you _might_ have a bad port or a bad cable.  From your description I cannot say for sure.  I have found WD Passport Ultra to work well for WSB targets.  Of course anything over 2 TB is wasted and may not work at all.

It is not bad cable or ports as I had to re-create the backup jobs twice now since installation. In other words, they rotate between WEEK1 and WEEK2 HDs and each HD uses its own usb cable and port.
We will find out more on Monday.

@Larry
I have both external USBs connected today and am ready for your instructions.

Sorry about my poor choice of "Instructions" word ...
On a working file server, I use only one USB cable and asked  the user to unplug the cable from the back of USB.
On this particular site, I left two USB cables plugged and asked the user to plug/unplug each USB HD to respective usb cables.
Should I just use one cable like the other site which is working?

Well, MS says it must work. And you say it works on another server but not on this one. Are you sure that you are connecting the correct drive to it during rotation and not the one from different server?

@noxcho
These two file servers are physically located 15 miles from each other at a separate business locations.

Let me do this. I will format both USB drives now and go thru set up process from the scratch. I will save the screenshots and post it after it is done.
They are doing a cloud backup, so erasing previous backups are not critical.
After setting up a new backup, I will check the destination area to make sure I see a drop down menu.

Backup-Setup.doc
OK. I finished the setting up a new backup job. I can see two USBs in Destination area.

I can have the user to rotate the USB once a day this week to see how it goes.
Or I can start running this backup job using "Backup Once" while only one of two USB HDs is connected at any given time throughout the day to see how it work?
What do you think?

OK. I will have the user disconnect one HD at a time and I will run the backup via Backup Once.

First backup ran successfully. I had the user disconnect WEEK1 HD and connect WEEK2 on the same USB cable. I started running "Backup Once" on WEEK2 and it is doing the backup right now. I will continue the test tomorrow at least a couple of times tomorrow between WEEK1 and 2.
I will post the result tomorrow.

Ok

Sounds good to me.  Let's hope that fixes it.

I ran the backup 4th time now.
First, right after creating the new backup job yesterday morning on WEEK1.
Second time, I ran "Backup Once" on WEEK2 .
Third time, "Scheduled Backup at 7PM" ran on WEEK2.
This morning  I started "Backup Once" on WEEK and it is well underway.

The only difference this time, compared to first time, is that I am using the same usb cable instead of using two separate cables for WEEK1 and WEEK2.
I don't know two usb cables confused WSB or what, but now I am seeing two USB HDs listed in Destination Usage section as you can see in the screenshot,

Now I think I can ask the user to rotate every Monday.

Consider rotating every day so that a complete restore of a destroyed system (and attached backup drive) is "yesterday" not "last week".  Consider three drives so that one is always out of the building.  I can assure you that if fire breaks out or the sprinklers go off or a 747 lands on the building, staff will not first think to grab one of or both of the two backup drives that are both on site for the switch.

Thanks for the suggestion.