I've had 1% patients ask me, "So what can you actually do as a DO? Are you a doctor?"
And then I've had 95% patients not even ask about the difference.
And then I've had 4% of patients who go out of their way to say they know what a DO is or have had one work with them in the past.
All I can say is that, we have made our lot in life by going the osteopathic route. This inherently means that you will have to explain what and who you are to people who don't understand. Don't get irritated or annoyed, it's just part of the fabric we have woven.
If you are in an MD setting, don't do OMT. There's a reason we have our own residencies - if OMT is what you want to do, then go down that path.
And I greatly dislike wearing a white coat, I would rather wear a suit everyday than deal with the lamecoat. It really just depends on your program. Some residents wear scrubs and no coat or scrubs + coat or jean shorts + lab coat.