Retrieve Time Machine back up from MyCloud to my new Mac

My iMac’s Hard Drive failed and I had to reformat the HD and re-install the Mac OS. It had been running on Mavericks (as far as I can remember) but now has Sierra. I also (possibly daft) gave it a new name. I have lost all my data. I have been trying to salvage what (I hope) was backed up on My MyCloud; I have managed to drag off a few individual files that I had manually dragged onto it, but the main back up I Have no idea how to restore. I have managed to drag off the .sparsebundle file (300gig) to my desktop, (where it has added a .zip suffix) but I can’t open that.
My iMac is on its last legs, I am sure, so, for the first time in my life have acquired a new one; but it is devoid of all my data as well as applications and info that was lost in the great crash.
Desperate for help! Read as much as I can but I only understand about a quarter of what I read, and fearful of trying things in case I lose or damage the backup.
Two specific questions that something I read made me wonder. Do I need to be trying to restore onto the same Mac (with the same name [I changed the name of the Mac when reinstalling OS] and/or do I need the same OS? I am hoping neither.
Do I in some way need to be restoring via Time Machine? Or via MyCloud? or via both? How would I do this?
Naively I just assumed a back up would allow me to find and drag off any files I had lost.
Thank you for listening!

Hi OliverKeen ,

I think you should contact the Apple Support for this.