The following version addresses the wishes from Kartik Shenoy's first comment, i.e.: Just hide two of the angles at each end of the link text:
(defcustom org-hidden-links-additional-re "\\(<<\\)[[:alnum:]]+\\(>>\\)"
"Regular expression that matches strings where the invisible-property of the sub-matches 1 and 2 is set to org-link."
:type '(choice (const :tag "Off" nil) regexp)
:group 'org-link)
(make-variable-buffer-local 'org-hidden-links-additional-re)
(defun org-activate-hidden-links-additional (limit)
"Put invisible-property org-link on strings matching `org-hide-links-additional-re'."
(if org-hidden-links-additional-re
(re-search-forward org-hidden-links-additional-re limit t)
(goto-char limit)
nil))
(defun org-hidden-links-hook-function ()
"Add rule for `org-activate-hidden-links-additional' to `org-font-lock-extra-keywords'.
You can include this function in `org-font-lock-set-keywords-hook'."
(add-to-list 'org-font-lock-extra-keywords
'(org-activate-hidden-links-additional
(1 '(face org-target invisible org-link))
(2 '(face org-target invisible org-link)))))
(add-hook 'org-font-lock-set-keywords-hook #'org-hidden-links-hook-function)