If a lot of results showing registrations for the same name come up, you may still be able to get your name registered If you plan to use the name for goods and/or services that are distinct from the other registrations.
After a free search, you may see a list of possible trademark conflicts. How do you know which of these conflicts are likely to be a problem and which ones aren't, and whether any of them will require you to choose a new trademark? In this situation, you may need a Comprehensive Trademark Search, which is much more robust.
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However, please note that applying for an already registered name always presents greater risks than applying for a name that isn't taken.