Can I petition for my wife if she came to the US under a different name?

Your wife's case is complicated and you will need assistance of a seasoned immigration attorney. Let us know if we can help,.

It depends. There is a waiver for certain false statements. A case like yours will require an immigration attorney. For a free consultation you may contact my office.

That is a very complicated situation. My understanding is that in most jurisdiction, entering on a fake name means that legally you were never admitted to the US. This makes it very difficult to apply for or obtain a green card. You need to make a consult with a competent immigration attorney to fully analyze this case, in particular to look at the current holding in your jurisdiction. The daughter's case is separate- since you are legally married you can sponsor your step daughter. However that will probably raise questions about your wife so again, use that consult!

The name is an issue, but a bigger issue is how she entered the US, with a foreign passport with another name, a US document or if she made a false claim to citizenship. If she used a PC passport, then you must see if she qualifies for a waiver based on an extreme hardship to a qualifying US relative.