Amongst the things I have made, I have these very cute backpacks for kids (in my opinion anyway).
They are easy to open & close and fit easily on a child's back. Once on the back, they are securely closed, and nothing can drop out, even if you cartwheel ;) They are fully machine washable and lined in white so it is easy to see what is inside. It is also possible to have them plasticized (for a swimming bag or just to be weather proof).
You can have them with just the child's name, or more practical, you can have one for each activity your child does with appropriate picture & lettering. Then store the necessary items for that activity in the bag. Meaning you can just grab the correct bag as you are running out the door to get your darling to ballet, music lessons, gymnastics, swimming... without leaving something necessary behind! ALSO, the bag will have your child's name on it, so others will know where to look for your child's items if you are not there for a moment - which happens if you have more than one child.
I saw the need for this while visiting my Sister last week. We had taken my older niece (Hannah) to swimming lessons & my younger niece (Grace) had come along to watch, but on route she fell asleep in the car! So my Sister got Hannah in & dressed in her cozzie (swimming costume for the non-South Africans) while I stayed with Grace asleep in the car. Then we switched so I could watch Hannah's lesson - she was very excited to have someone new to witness her swimming prowess!
Problem was, when Hannah got out of the pool, I had no idea which of the bags belonged to her, and she was not sure either - Mom always sorts this part out. So I had to wrap my shivering niece in my down jacket, leave the warmth of the indoor pool, and run, jacketless, back to the car to ask the all knowing mother!
A personalized swim bag would have been just the ticket!