You don't need to change into special clothes for a walk in the park and it's the same with cycling, unless you want to. It's normally a good idea to wear a cycle helmet and something to protect you if it rains. Bright clothing is good to be visible in the daytime and reflective strips are good, especially at night. Some people like to wear special cycling clothes, but you don't have to. Mudguards are useful to keep your clothes clean.
It's always a good idea to pack a spare something and if you're cycling some distance to work. Your workplace may have showers and changing facilities so you feel more comfortable.