After Arthur Eddington confirmed gravitational lensing (the light from another star is bent by gravity) in 1919, a major prediction of General Relativity, his once obscure theories that were only known within the scientific community, were reported as the greatest breakthrough in Physics since Newton by all of the world's largest newspapers at the time.

In 1921, Einstein went on a lecture tour in the USA, delivering several lectures on General Relativity at Princeton and Columbia. These lectures, which were given by Einstein in German, but many were anxious to see and hear the man who had revolutionized science. Thus the lectures were filled to the brim with people who just wanted to experience history, not necessarily understand his theory. When Einstein went to visit Harvard (he didn't lecture there), he was greeted at the train station by thousands of people looking to catch of glimpse of him.

Thus, I would argue that Einstein was probably a greater celebrity during his lifetime than Hawking was.

Throughout his life, Einstein would be amused with the sort of "god like" status he was given by journalists, and he remained aloof and uninterested in praise. At a reception in the National Academy of Sciences, Einstein listened to long speeches from various people honouring him, including the Prince of Monaco. Einstein became bored as the evening droned on, turning to a Dutch diplomat and saying, "I've just developed a new theory of eternity".

In 1923, Einstein gave a lecture tour in Japan, 2500 people went to listen to his first 4 hour long lecture (which he gave in German), which was followed by Einstein being received by the Emperor and wife. Einstein was, as always, amused by the reception, telling his wife Elsa; "No living person deserves this reception".

I am not going to list all of times that Einstein made sardonic comments about his own celebrity (you can read his biography for that, and I recommend you do!), but it's clear that he felt the attention he received was over the top.

One more quote;

"Since the light deflection result became public, such a cult has been made out of me that I feel like a pagan idol. But this, too, God willing, will pass."

In regards to his appearance, there were no doubt, cartoons emphasizing his appearance, his shock of grey hair and his shabby clothing. It quickly became an integral part of the image he was known for.

In regards to using Einstein as a noun, the Online Etymology Dictionary lists its earliest usage as a type name dating from 1920.

Sources:

Einstein: His Life and Universe by Walter Isaacson