Worried about employment background check
I have a first-round interview coming up next week and it's my first of recruitment season. I know I may be thinking too far ahead in terms of background checks since I believe that is at the end of the process once you get offered, but this just popped into my head and I just want to get clarity on how to address this if I need to before I go insane.
So last summer, I interned for an individual who's worked in investment banking for 30 years (IB). The person (my boss) I worked under had their "own" bank, and then also is employed by a global/cross-border M&A advisory firm that has individual bankers stationed in major cities across the world. I ended up working for them throughout the school year and am still working with them, and recently began assisting my boss with work for the cross-border firm that required I get a corporate email address.
When I got the corporate email address, I proceeded to change the name of the bank on my resume from the one-man shop to the bigger firm and this is what I'm worried about. I've been working under this person since June, and honestly never questioned what "firm" the work I did was for. I honestly don't know for sure and should probably check in about this as this could have an effect on what I do. Maybe not. I always just had the name of the one-man shop. I'm just worried about the bank I'm interviewing for calling the big firm and asking "has _____ worked for you since June" and they say no and I'm fucked.
How are employment verification background checks done? Will they ask for me to provide contact information or go and find that information themselves? If it's the former I think I'm fine cause I didn't lie about the work that I did so I'm happy to give them my boss' phone number. I'm just worried about it being the latter.
Please help looking for any sort of advice here.