This is The Astounding Dr. Amizov by R. F. DeBaun, first published in the January 1974 edition of Analog Science Fiction/Science Fact.
As you said, the titular character was Dr. Igor Amizov, a fictional sci-fi writer in the mold of Isaac Asimov:
Dr. Igor Amizov.
In the pantheon of science-fiction greats that name stood above all others. Jules Fern, H. G. Welps, Brad Raspberry—none of these could match Amizov's imagination, his wit, his style, or his sheer prolificity. Who could ever forget "Crustacean," "Crustacean and Umpire," and "Second Crustacean," his classic trilogy about a race of giant crabs who came out of the sea to win the World Series? Or his moving "I, Rowboat," the tragic saga of an intelligent dinghy in a world of hostile humans?
It's noted that Amizov is also an accomplished scientist:
And Amizov's genius was not limited to fiction. His fertile mind had parlayed a Ph.D. in biochemistry into scores of books explaining virtually every scientific discipline to the layman. Astronomy, anatomy, mathematics, physics, botany—no scientific stone was left unturned in his myriad works.
The protagonist, Paul, is an aspiring sci-fi writer who wishes to show his recently completed first novel to Amizov, hoping Amizov might put in a good word for him with a publisher. However, his nerves get the better of him during his first meeting with Amizov at an auditorium, and he fails to make the desired impression.
Three months later, he decides to confront Amizov at his home, hoping to convince him to take another look at his novel. After climbing over a wall into Amizov's garden though, he encounters not just one Amizov, but five of them. Shortly thereafter, they explain that Amizov cloned himself five times, and that this is the secret of his success.
"Which one of you is the real Dr. Amizov?"
"We are all the real Dr. Amizov," said number 5. "Although you'd probably get some argument from number 1. He likes to think the rest of us are copies made in his image."
"Copies?"
"It's not, easy to explain. You don't happen to be a biochemist, do you?"
"No, I'm afraid not."
"Do you by any chance know what a clone is?"
"The secret to the Amizov success is that six heads are better, and more prolific, than one.