Try the following i got the exact result that you were expecting.

newdir=`basename $BackupLocation`
BackupLocation=$BackupLocation/$newdir$(date +%w)

################################################
$ > BackupLocation=abc/namsih
$ > newdir=`basename $BackupLocation`
$ > BackupLocation=$BackupLocation/$newdir$(date +%w)
$ > echo $BackupLocation
abc/namsih/namsih5
$ >
################################################

Let me know in case of any concerns.

Thanks,
Karthikeyan.