Може ли притежателят на търговска марка да вземе генеричен еднословен .com?

For example,

Let's say I'm interested in buying "dove.com"

And there is a company called Dove that has a trademark for "Dove" to sell soap

Can Dove, the soap company, claim the rights to dove.com even if I don't use it to sell soap?
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Let's say I use it to sell technology and make sure there's no confusion between my company Dove and their company Dove.

Is there any legal risk here?

Yes, there is massive legal risk. Even if you do not sell soap, and even if you take active steps to ensure zero consumer confusion, a famous trademark owner like Unilever (the maker of Dove soap) can still successfully challenge you under the Anticybersquatting Consumer Protection Act (ACPA) in the US, or through Uniform Domain-Name Dispute-Resolution Policy (UDRP) proceedings globally.

In fact, holding a domain name identical to a famous global brand without a legitimate prior right is precisely what domain dispute frameworks are designed to penalize.