What's the best way to reject an offer/withdraw your application?

I was lucky enough to receive an offer from a buyside firm that I have since accepted, but I was wondering what the best way to reject an offer was. Also received offers from a couple sell-side positions, but I declined them and spoke to them on the phone letting them know I was thankful for the opportunity, but when they would ask which company I was working for, I declined to name them stating that I wanted to keep it private while everything was being settled, but I did say industry and position. Am I just overthinking this? Is it standard to give the company name once you've cleared background checks etc? Thanks