>
> Would allowing a regexp solve the expression \alpha-\beta, \alpha+\beta, 
> \alpha/\beta, so that \alpha and \beta are prettified seperately?
>

That's not necessary.  Just follow Stefan's advice:

(defun texinfo-prettify-symbols-compose-p (start end _match)
   ;; We know the matches all start with a backslash and end with
   ;; a word-element.
   (not (or (memq (char-before start) '(?\\))
            (memq (char-syntax (or (char-after end) ?\s)) '(?w))
            (nth 8 (syntax-ppss)))))
(add-hook 'texinfo-mode-hook
           (lambda ()
             (push '("\\alpha" . ?α) prettify-symbols-alist)
             (push '("\\beta" . ?β) prettify-symbols-alist)
             (setq prettify-symbols-compose-predicate 'texinfo-prettify-symbols-compose-p)
             (prettify-symbols-mode)))

This does what you want.