(setq auto-mode-alist (cons '("\\.md" . markdown-mode) auto-mode-alist)) 

That \\.md should be \\.md\\' otherwise it'll match every filename containing the sequence .md anywhere.

The regexps in auto-mode-alist are matched against the entire filename, so you can use the same technique for COMMIT_EDITMSG. You would also normally use add-to-list to update it.

(add-to-list 'auto-mode-alist '("/\\.git/COMMIT_EDITMSG\\'" . markdown-mode)) 

(setq auto-mode-alist (cons '("\\.md" . markdown-mode) auto-mode-alist)) 

That \\.md should be \\.md\\' otherwise it'll match every filename containing the sequence .md anywhere. (I.e. You already weren't limiting your usage to just matching filename extensions. For instance /home/alper/.mdir/foo/bar.c would match your pattern.)

As you can see, the regexps in auto-mode-alist are matched against the entire filename, so you can easily use it to match your COMMIT_EDITMSG files.

One would normally use add-to-list to update the variable:

(add-to-list 'auto-mode-alist '("/\\.git/COMMIT_EDITMSG\\'" . markdown-mode))