Hi,
If you are providing face to face training then the place of supply for business to business will come under the general rule of services and so will be subject to the reverse charge by the business where they belong in the EU.
The reverse charge will not apply to the business customer in the US but we would recommend checking with the American authorities about any local tax requirements.
Place of supply of services (VAT Notice 741A)
If you are supplying business to consumer sevices of training then the place of supply will be where the training takes place and so there could be requirements to register in the countries in the EU where the training takes place.
Place of supply of services (VAT Notice 741A)
You can't register for One Stop Shop in the UK for supplies of services but please refer to the European Commission website.
Declare and pay in OSS
Thank you.