The EU single market has resulted in the number of companies expanding beyond their national borders.
As of June 2017 the business registers of all EU countries have been interconnected and become searchable.
In accordance with Directive 2012/17/EU this service is to cover the business registers of all EU countries as well as Iceland, Lichtenstein and Norway.
On the European e-Justice site, you can search European trade registers for companies (BVs and NVs).
European e-Justice is part of the European Commission. In time you will be able to search in all countries within the EEA with one search, but not all countries support this yet.
The other European countries that do not belong to the EEA also almost all have a comparable register.
Obviously, the legal basis of the EU directives does not apply to this.
Many countries are seeking to link up with this and have comparable regulations.
Link for more information