OK that is good news..that it now can be configured.
Is there something I can do to make it realise it's the same disk or will I have to delete the whole disk and then do a full backup again?
Even if you gave it the same name things do get confused..
You do not need to delete the current backup.
In Time Machine all you need to do is select the "new" disk.. as the target for your backup.
This is from an earlier post I did. Time Machine has lost connection to a backup on a different brand router but that makes no difference..

TM counted down 120sec to start a backup.. and then mounts and checks the disk.
You will see TM now goes into a very long period of preparing the backup.. what has happened is that TM discovered the existing backup.

The log shows why.. it is doing a deep scan.
Starting manual backup
Attempting to soft mount network destination URL: afp://ray-local@RT-AC3200-82F0._afpovertcp._tcp.local./Backups.backupdb
Mounted network destination at mount point: /Volumes/Backups.backupdb using URL: afp://ray-local@RT-AC3200-82F0._afpovertcp._tcp.local./Backups.backupdb
Checking for runtime corruption on /dev/disk2s2
Disk image /Volumes/Backups.backupdb/z87proimac.sparsebundle mounted at: /Volumes/Time Machine Backups
Network destination already mounted at: /Volumes/Backups.backupdb
Disk image already attached: /Volumes/Backups.backupdb/z87proimac.sparsebundle, DIHLDiskImageAttach returned: 35 (Resource temporarily unavailable)
Disk image /Volumes/Backups.backupdb/z87proimac.sparsebundle mounted at: /Volumes/Time Machine Backups
Backing up to /dev/disk3s2: /Volumes/Time Machine Backups/Backups.backupdb
Forcing deep traversal on source: "asusz87pro" (device: /dev/disk0s2 mount: '/' fsUUID: 2BB3E4A1-CE4C-350F-B8E8-E69BB22A5DE1 eventDBUUID: 1A326CD6-8C1A-467B-9FB1-3A628959CEFA)
Deep event scan at path:/ reason:must scan subdirs|require scan|
Running event scan
initial consistency scan for '/'
Depending on the size of the backup and speed of the network connection. (if it is network target..) it can take a long time..

It took 20min to complete check of 120GB boot drive backup on fast network.. multiply your disk size by the time. Divide by whatever fraction your network speed is less than 1Gbps. For wireless divide by another 0.5 to include reality over hype. (Maybe 0.1)

Assuming the scan comes up Apples.. (used to mean all good A+)..
The backup will proceed to do a simple incremental.
The log will show now what has happened.
Finished scan
Saved event cache at /Volumes/Time Machine Backups/Backups.backupdb/z87proimac/2018-01-02-113204.inProgress/62C502BA-C5CB- 488F-AB71-E0D44D3EF25F/.2BB3E4A1-CE4C-350F-B8E8-E69BB22A5DE1.eventdb
Will copy (152 MB) from asusz87pro
Found 810 files (152 MB) needing backup
443.7 MB required (including padding), 287.52 GB available
Copied 1129 items (152.3 MB) from volume asusz87pro. Linked 4637.
Created new backup: 2018-01-02-115130
Starting post-backup thinning
Deleted /Volumes/Time Machine Backups/Backups.backupdb/z87proimac/2018-01-01-104923 (62.1 MB)
Post-backup thinning complete: 1 expired backups removed
Backup completed successfully.
Ejected Time Machine disk image: /Volumes/Backups.backupdb/z87proimac.sparsebundle
Ejected Time Machine network volume.
And the previous history will be noted as per before you reconfigured.

If this doesn't work for you we need to get harsher and do some more dirty stuff.
As a btw my recommendation now to everyone on Sierra and later OS.. do NOT trust Time Machine.. it is unreliable at best.. broken at worst.. and you can discover it wasn't backing up properly anyway without any indication.
Use a third party like Carbon Copy Cloner..
If you really must use Time Machine use it to local drive plugged into the computer .. eg USB. Since Sierra network backups are too problematic.
How to reset Time Machine.
To go a step further you can start Time Machine afresh.
Apple made no provision to do this.. so you need to get down and dirty.
Delete TimeMachine.plist
Macintosh HD > Library > Preferences > "com.apple.TimeMachine.plist"(delete this file or rename it)
In Finder locate the main Library and Preferences. (you might need to turn on view hidden files).
I renamed the existing file old.. and reboot the computer.. when you start Time Machine again via preferences it will recreate the plist.

Then just configure Time Machine to use the previous disk.. it will still take a long time to deep scan the existing backup but should continue the backup.