Numbering of properties is preferable to naming as it gives a clear indication as to the location along the street, however it is acceptable to allocate a name but only in certain circumstances.
This will depend on which Acts have been adopted by the local authority. The First Scheme for example states all addressable objects must be numbered by the local authority. This includes new residential, commercial and industrial buildings and conversions of existing buildings. However, the 1939 Act for London and other local acts allow for naming too. The 1972 Local Government Act allows for incidental naming as long as there is a number in place.
It may be that there has already been set in the street where all properties have been named and not numbered historically and therefore numbering the property would be inappropriate regardless of the acts that are adopted by the local authority.
Either way, buildings should be numbered/named to the street which was the last used or provides direct access to the entrance to the property.
See Acts and Legislation - The First Scheme and Property Naming