This explanation is a bit weak and far fetched, as it relies on the Tyrell Corporation retraining Deckard but not changing his name. (Imagine if Roy had called him "Mr Smith"!). This makes the Deckard/Zhora confrontation more interesting: she would have recognized him, and would be wondering if he was having a joke or not. When she realized that he was for real, she clobbered him. This could also give Bryant an excuse for getting the number of escaped replicants wrong.
Different versions of the script have Deckard as a well-known Blade Runner, so in that case it would be reasonable for Batty to know about him. A likely explanation is that Leon was within earshot when Deckard showed his ID to a cop and gave his name; in an earlier script, Batty then had Leon go after Deckard for killing Zhora.
In Hampton Fancher's script dated 7 January 1980, Bryant tells Deckard that the replicants may have tapped into the ESPER computer and that it will take about a day to secure the system. Later, at Sebastian's apartment, Batty tells Pris and Mary that Leon and Zhora are dead and that the police have discovered he has been tapping into their computer. He informs them that he can't monitor what the police are doing anymore. This is what causes Pris to say, "Then we're stupid and we'll die," and why the replicants are expecting Deckard to come for them.