It won't raise any red flags with them. They will see that you have a profile, that's it.
You can have more than one checking account open. All of the branches are linked.
Check the guidelines and see how long you have to keep the account open. For mine it was two weeks. If you keep it open longer, find out what you need to do to avoid the fees (balance, direct deposit, swipes, etc.).
I had a savings account that was required to stay open for 6 months. I had the minimum in there to avoid any fees. I was able to do many other shops with that MSC and others. The only reason I closed it was so that I could do another shop of the same type.
"I told myself to quit you; but I don't listen to drunks." -Chris Stapleton