ecommerse sole proprietor changing business name

You want to avoid misrepresenting your qualifications. Calling yourself either "ID Doctor" or "Medical ID Doctor" may be problematic, since a very fast internet search turns up that "ID Doctor" is a common term for "Infectious Disease Doctor."

That's not to say that you *can't* use the name, as long as it's not taken for a similar business selling in an area that you sell. (If there are other businesses with that name, but your business paths do not cross, you can probably use the name but not trademark it; to trademark it, it should ideally completely free and clear.) Just make sure to not actually state or imply, even by accident, that you have a medical degree to go with the business name--e.g. proof your marketing material extra carefully.

However, while you probably could use it if you chose, the fact that infectious disease medical doctors are called "ID Doctors" probably means you shouldn't use it. Being associated with infectious disease is rarely a marketing plus, and it might be too easy then for someone to assume that you are in fact a physician, which may lead to incorrect expectations.

I think you need to be very careful about this, and it might be better to either keep your current business name or come up with another idea.  Many states have laws about using the word "doctor" to protect consumers from being misled, and those laws almost certainly are different from one state to the next.  With an internet business, you would have to steer clear of names that would be considered unlawful in any place you sell or market your products, so that means that you would have to obey the toughest rules -- whatever those might be.  It would probably take a lawyer two or three days at least, to research that for all 50 of the United States -- and then there's Canada, etc.

There's a landscaping company known as "Lawn Doctor."  That's not capable of misleading anyone with half a brain.  But "Medical ID Doctor" sounds dangerous, to me.