>>> 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.
>
> That is not completely correct because for "\alpha-\beta", only \beta is 
> prettified.
>

No, \alpha-\beta is prettified correctly.  Tested with Emacs 25, 26, 27 
and 28.