A trademark protects any mark that identifies your product or service. The mark can be a logo, a name, a phrase or something similar. If you use an original trademark in commerce, you’ll automatically have rights to that mark in your region. However, registering your mark with the U.S. Patent and Trademark Office will give you greater protection, along with eligibility for more damages if you sue someone for infringement.
A trademark is a legal right to exclude others from using the trademark as a designation of origin. A trademark then serves as an indication of origin, as only the trademark owner (and their licensees, under some circumstances) would use that trademark in connection with goods or services. Usually, when advertising, one would want to associate the trademark, so that advertisement viewers will know what product/service they should ask for. If you see something and you instantly know where it came from, that’s probably a trademark. If you see someone walking down the street in the U.S. with a particular color of short-sleeve shirt, you might assume they work for a particular parcel.

What is a legal business name?

Legal business name just means that you have to actually register it with your local government authority which inturn gives you a tax number. Now most banks today require this number to open a real (legal) business account! Most laws state that you can run a business under your name and at the end of the year you declare this income as extra income. You may call it your business. But in Paypal’s eyes, this is not a “legal” business. They want you to have that tax number and a business account to help cut down on fraud. They assume that by you registering, you had to go through steps to be credible!

Using the word Einstein

Using the word Einstein in a business has more to do with trademarks than copyright. You should consult a trademark attorney. My hunch is that if your business has nothing to do with special relativity, the atom bomb, or anything Albert Einstein was involved with, and if you don’t use his likeness in any of your materials, you’ll probably be okay. Especially if your last name is Einstein. If your last name is NOT Einstein, it begs the question: Are you trying to confuse people so you can cash in on the good name of the famous scientist Albert Einstein without paying his heirs? If so, that’s probably not okay. There are few registered trademarks in the name “EINSTEIN”. You may check. Mostly EINSTEIN is used in education related brands. As such Ministry of Corporate Affairs may not approve your EINSTEIN as well. Because, there are trademarks registered. They may refuse the trade name.