You're supposed to use common sense. Don't do anything blindly.

IFR on a missed approach (one type of go-around), I follow the missed approach procedure, and will deviate only in the event of a conflict or ATC instruction.

When doing light airplane VFR flying, if I go around, I offset to the right of the runway so long as it won't create a hazard with obstacles, other aircraft or runways, etc. If I have to go around, it's invariably another aircraft that didn't get off the runway, or that entered the runway. I offset to keep them in sight, and only just enough.

If it's a right pattern and I offset to the left, how am I going to see the aircraft on the runway or that elected to take off (or that went around ahead of me)? If I'm overtaking slower departing traffic or slower traffic that's going around, should I not be to the right to overtake? Common sense.

Why I'm going around may have a lot to do with my actions. Offsetting may not be my priority.

At a towered runway, I may find it advisable to communicate the offset to ATC, or even get permission to offset, turn early, do a dogleg away from the runway, etc. It depends on the circumstance.

Fly the airplane.