I'm going to address the problem of sharing the name with the company's owner, as motosubatsu's answer addresses the issue of the company's reputation fairly well.
One option is to slightly change your name to distinguish yourself from the owner - add a middle name or initial, or maybe you use a nickname you'd be happy to go by. So instead of just being "Joseph Schmo", you would be "Joseph P. Schmo", or "Joseph Percival Schmo", or "Joey Schmo", or maybe even "J. Percival Schmo". The trick is to change this consistently everywhere you have control over - resume, cover letter, personal website, LinkedIn, even social media. You want to create a consistent digital identity that is clearly linked and separate from the owner. You won't have control over everything that's out there, but as long as you can get interviewers to pause long enough to verify your position, then you've succeeded.
To be more direct about it, you might make a side comment in your cover letter. St some point in your letter you will mention your current company, at which point you mention the owner.
During my time at Acme Corp (whose owner I happen to share a name, though no relation), I worked on ...
And then continue on to talk about what you did there. You never want to talk badly about a (soon-to-be) former employer, but instead focus on your experiences and contributions that will be beneficial in the new job.