In fact I think it depended a lot on "alien" status.
That placed an obligation on "aliens" to register name changes (personal and business)
The legislation is here
Bear in mind when reading that the 1919 legislation particularly was to a considerable extent specifically targeted at Jewish Marxist terrorists operating in and around London and causing considerable mayhem, murders and robberies in furtherance of their cause.
The largest terrorist standoff on British soil remains the siege of Sidney street which resulted from the activities of these individuals who caused so much disrepute to our community and who drove this legislation. An earlier motivation of the Act (of 1914) was motivated by a fear of German spies (German Jews felt compelled to announce their support for Britain in 'loyalty letters' to newspapers).