When you only leave link in the Name field, Is this link considered as a comment backlink by google bot? or Should I leave a link in the Comment field?
In general, Google does not count comment backlinks from WordPress. WordPress marks them as
nofollow links, which ask Google to not pass link juice.
That said, Google has recently changed
nofollow from a directive to merely a "hint", so while unlikely, it's not completely impossible that these author links could shape SEO in some way.