I'd want to correct them on the company name because it can make a difference. My friend bought her baby a Graco carseat (grey-co) but said Grecco (bless her heart). She does buy some ritzy unknown brands so I assumed I heard right only to see that it said Graco. But if I was looking for the product by that name it could throw things off.
As for the name, I have terrible short term memory so I completely understand. If it's a one time meeting or something I'll let them say whatever but if I'm going to see them again I politely say "oh, it's Christina" & smile. And if I'm not 100% sure on theirs, I omit the name.
