Apparently, Bonham Carter stated in an interview on a Dublin radio station in February the following:
So what's their daughter's actual name?! She was born this past December.
Tim [Burton] and I haven’t decided on a baby name yet, because Tim has been out of the country promoting Sweeney [Todd]. I want to get a chance for him to spend time with her and see what name feels right.
Apparently on the internet she’s called Indiana Rose! [laughs] I don’t know where it’s come from but it can be that till she’s been named properly [laughs].
In the mean time, here's a photo of her with her mother:
Photo from Helena-World