Yes, you can have same company name and a trademark. Here, you can register your company name under trademark law. On other hand, if you have already registered/ applied for a trademark, you can use it for your company’s name.
In both cases, you are required to get approval of the respective registry.
You are required to make availability check for both company name and trademark registration.
Take a note that you cannot use an existing trademark for the name of your company if it is owned by someone else, unless you take their permission, or obtain a license.
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