>Edit: Also, if anyone requests reference checks from your current employer, you should say no. It's not standard practice to check current employer, only prior employers (at least in the US).
Question for you: One of the previous companies I worked for changed their name after I left. The company is still searchable under the old name. Should I list the new name, or old name on the resume? I feel like it's not really my problem, but also is my problem, you know? It's a weird thing. I'm not sure how common of a problem this is.