I have done these at three large banks (some several times) and at what you referred to as the no-name bank. All are easy money, did not affect my credit at all, and were closed with ease. I am in the middle of doing a group of 5 across 3 banks, all repeats of ones done a couple of years ago. For multiple savings account, I just say that I am saving for different trips of other large purchases and ask if I can give each account a "nickname" to help me to manage them. So, at 3 different branches of Bank A I may have accounted named: Maine vacation, new car and deck refinishing.
Based in MD, near DC
Shopping from the Carolinas to New York
Have video cam; will travel
Poor customer service? Don't get mad; get video.