Whether a person having multiple business verticals in a State or Union territory can obtain different registrations for each of such vertical

Yes. As per proviso to Section 25 (2) of the CGST Act, a person having multiple
business verticals in a State or Union territory, may obtain a separate registration for each business vertical, subject to such conditions as may be prescribed.

(ICAI FAQ PUBLICATIONS 06-09-2017 REGISTRATION: FAQ NO. 4)