At the end of episode 220 of Detective Conan, "The Client Full of Lies", Heiji appears and explains the reason behind the fake name "Reiko" to Conan that it was to conceal the fact that his mom is from Osaka.
But that doesn't explain why she has to lie about her being good at cooking and her allergy to dust. If she were to hide her identity, she need not lie about the cooking and the allergies. Conan wouldn't be able to find out even if he knew that she was from Osaka since it was his first time meeting Heiji's mother.
Why did she have to go that far? Or was it part of her test for Mouri to figure out her real identity?
Even if it's the case, I bet no one's going to be able to deduce that she is Heiji's mother because first, it's impossible to even know the true identity of a person just by knowing her hobbies or skills. Unless she has a distinctive quality in which the Hattori's are famous for.
Second, Conan did not even know a thing about Heiji's mom. The test was actually for Shinichi but since he wasn't there, she tried Mouri instead. No matter how good Conan's deductions were, it was impossible for him to expose her real identity as Heiji's mom and her real intentions. They were even surprised when she revealed her true identity as Heiji's mom since Heiji didn't even look like her.
So, why did she have to lie about all the stuff?