For all of the minor modes that I use, I enable them globally. This may change in the future, as can anything, but for now I have no need to know which minor modes are enabled, because the answer is "All the ones I like." Diminish is a package that allows the replacement or omission of mode names in the mode line.

(use-package diminish
  :ensure t
  :pin melpa-stable
  ;; Diminish built-in modes we've already enabled.
  (diminish 'flyspell-mode)
  (diminish 'visual-line-mode)
  (diminish 'whitespace-mode))

Since we have not yet installed any new minor modes, we will diminish only those which are part of the base system. In future entries we will use :diminish in use-package to include packages in the list that Diminish affects.