Any trading entity (an individual, a partnership or a limited company) is obliged to register for VAT if its total turnover from taxable supplies exceeds the relevant threshold. Once registered, it is issued with a VAT Number.
Certain things follow from this:
(1) all of an entity's supplies need to be considered for the purposes of registration - even if the entity carries out more than one trading activity
(2) as a result, a trading entity will only have one VAT registration number (which answers your question)
(3) there are regulations preventing a business from being artificially split into a number of separate entities in order to avoid registration