Can two companies that are offering the same services in Benelux have similar company names?
Both company names have been registered with www.BOIP.
There are a couple of dimensions to this question that its wording conceals.
First, one of the real questions is not "can two companies . . . have similar company names", but "how similar can the names of two companies be without either of them having a right to stop the other company from using a name similar to their name."
I suspect that the relevant legal standard is "confusingly similar", which is an international standard in trademark law, but ultimately, that is something that has to be decided on a case by case basis regardless of what the standard in the law is there.
Second, the actual names in question probably matter. Some names are generic, like "butcher" for a butcher's shop, and can probably be used by pretty much any business even if it is virtually identical to another business. But, if the name is not generic or descriptive and has developed an association with a particular business, it might be possible for one business to protect from another violating business. This is also a basis and mostly universal concept in trademark law internationally.
I suspect that www.BOIP is probably operated on a basis that as a default allows any name that is not exactly identical to be registered and then leaves disputes over similar names to the courts if any affected business wants to raise the issue. Many nations and many U.S. states operate their business registration systems on this basis, because it is much easier to administer that a system that tries to pre-evaluate which business names are too similar to each other in the same industry in advance.
But, I don't have access to resources that could provide a more definitive answer.
Yes, that is possible. Article 2.14 of the "Benelux-Verdrag inzake de intellectuele eigendom" states that objections have to be filed within 2 months of the second registration. If this does not happen, the two registrations are allowed to coexist.
(Note that the title assumes this is EU law. It's not; the relevant rules are specific to Belgium, Netherlands and Luxemburg.)
In the UK, you would have to register your company name with companieshouse.gov.co.uk. They have some rules which names are not acceptable at all, and they won't accept your name if there is an existing company with a name that is similar enough. Basically, your name is either accepted and you are fine, or it is not accepted.
They do NOT look at company names elsewhere in the EU, or elsewhere in the world. I have a company in the UK, and there is another company in the USA with the identical name, and there is no problem. I could have picked the same name as one of these two companies.
But that is only for creating and registering a company. Companies can have trademarks, only one company can have the same website address obviously, so even when you have the company name legitimately, there may be restrictions.