If someone is using your trademark, then you have every right to fight to stop them. Sometimes, names are similar or spellings are different, but if enough similarities exist, there could be a case for trademark infringement.
Often, it's just a coincidence that names are similar. Take this case from May 9. Dr. Dre, a Grammy award-winning rapper launched a lawsuit against a doctor called Dr. Drai. The spellings are different, but the names sound the same.
Dr. Drai, whose full first name is Draion, described himself as being a media personality and obstetrician/gynecologist. He offers advice online with a video series and wrote a book. He also appears in public, where he is a motivational speaker.
The U.S. Patent and Trademark Office heard the argument that the two could be confused, but it disagreed. It believes that the trademarks do not violate each other, since the goods and services provided by each of the men are different enough not to be confused.
Additionally, Dr. Drai was referred to as Drai as a nickname; it's a name his friends, colleages and others use when speaking to him. He sought protection for his name through the USPTO, but Dr. Dre, the rapper, objected. Furthermore, the USPTO determined that since Dr. Dre is not an actual medical doctor, there was little likelihood of confusion with Dr. Drai, who would be providing medical services.
If you're worried about a trademark violation, you can pursue a lawsuit as well. It's a good idea to have your attorney review the case to make sure it has a strong base of facts and evidence.
Source: Forbes, "Dismissed! Dr. Dre Loses Trademark Fight Against OB/GYN Dr. Drai," Michelle Fabio, May 09, 2018