Can I remove Windows Boot Manager from dedicated Ubuntu computer?

It is normal to have two ubuntu entries. One is shim and the other grub. You can see the details of each with :

sudo efibootmgr -v

You can delete the /EFI/Microsoft folder in the ESP - efi system partition and then delete the UEFI NVRAM entries. If you leave the folder, UEFI will often find the boot files & add them again to UEFI boot menu. It can depend on how you have mounted ESP on where it is. Inside install it is /boot/efi/EFI/Microsoft. But newer versions of Ubuntu make ESP write protected with 0077 mount permissions in fstab. Change to defaults like 14.04 and remount to make sure no errors before rebooting and you have to reboot for new permissions on /efi to take effect:

sudo nano /etc/fstab
sudo mount -a

14.04 fstab entry defaults

UUID=FD76-E33D  /boot/efi       vfat    defaults        0       1

16.04 fstab entry umask=0077

UUID=68CD-3368  /boot/efi       vfat    umask=0077      0       1

This discusses the removal of an entry. Just be sure to use the Windows one:

How do I remove "Ubuntu" in the bios boot menu? (UEFI)

Delete entry change XXXX to correct entries. Some UEFI require all 4 HEX char, other just need 1 or 2 significant char.

sudo efibootmgr -b XXXX -B

details on efibootmgr commands:

man efibootmgr

http://linux.die.net/man/8/efibootmgr