Avoid current employer being contacted for background check

I would assume that when companies do background check before hiring, they wouldn't contact my current employer. What about past employers who are related to the current one? My situation is that my employer A is a parent company of my previous employer B. Legally A and B are two separate companies, but they share a lot of things - shared office space, same people in HR, same upper management, some teams in A and B have common roadmaps and sprint planning. I have stayed with B for several months before deciding to change teams, which meant joining A. So de facto it was an internal transfer, but de jure it was a new employer with a new employment contract. So, if company B is going to be contacted for background check, then obviously my current employer A would know it, since the HR is shared among the two companies. How should I go about it when mentioning my employment history in a resume? If my resume mentions B as my previous employer, my current employer A might know that I am job hunting because B might be contacted for background check. If I say that I have been at A all the time, even those several months when I was at B, technically it's not correct and might be seen as lying. If I leave out from my resume the period I was at B, it might look like I was unemployed for several months. TC: 110k #hiring #hr #backgroundcheck