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You can trademark a name or a logo. So, yes, a trademark can be used as a company name (e.g., Hershey and Hershey bar). It does not matter if you use a different name for your company or product, except that if you want to protect both names, you would have to trademark both names.
For an on line site offering both product and services, you would have to get a trademark for the product and a service mark for the services. The name can be the same but the categories in which you trademark the names would be different.
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