If someone else has been using it in commerce before you then their rights will predate yours. In the USA it comes down to "first in use," and you've acknowledged that someone else has started ahead of you. Even if you move forward and attempt to formally trademark it ahead of them.
I'd consult with an attorney on this before moving forward. If you intend to build a business and protect your IP (which you should), you should make sure that you are doing it the right way and not risking any infringement or other issues surrounding your right to use the name/logo.
Legal disclaimer: I am licensed to practice law in the state of Washington and the answer provided above is for general information purposes only and should not be relied on as specific legal advice. This answer does not form an attorney-client relationship. You should consult with an attorney of your choice to fully advise you about your legal rights and obligations.
I agree with Attorney Camm. Even if the first user hasn't trademarked his logo, his right to use it supersedes yours and you can be sued. Consult with an IP attorney on how to avoid a lawsuit.
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I agree with the previous answers, however it should be noted that common law trademark rights are limited to the geographic area in which the mark is used. The prior user of this non-registered mark could only enforce his/her/its rights against you in the geographic region in which the mark has been used.