As the latest chapter states, Isshin's name was Shiba. Of course you posted this thread before the latest chapter, but still even in that case it was perfectly explainable why Kurosaki was the name of Ichigo's mother.
When Ichigo popped up in SS, no one made, or in the least didn't show it, the connection between Ichigo and a previous captain of roughly 20 - 25 years ago. I mean suddenly an unknown shinigami comes along that has the same name as a relatively seen recent captain that disappeared (I doubt Isshin went away with the approval of SS). So yeah even without the recent chapter it would be a logical assumption that Ichigo took his mothers name to avoid troubles.