What are effective ways to label children's clothing? It seems that most forms of writing will wash off in the laundry and also it's difficult to write in small font handwriting to fit on the small available space.
If you use permanent markers like Sharpie brand, particularly fine point ones, they usually don't come off in the wash. The school my son goes to uses them to mark their house clothes if kids get their clothes dirty without any extras at school. You can write on the care tags if your clothes have them or you can write them in a hem where the cloth is two-layers thick and it shouldn't bleed through unless you're really heavy-handed... and if it's in a hem (waist hem, for example) it probably won't be too noticeable anyway.
Something like this:
We splurged on buying fabric labels from a custom label company... the sorts crafters/sewers use to put their brands in clothing. We sew one end into the bundle of existing labels (either in the side seam or neck band) and it's good to go. Our son doesn't have any reactions to them that we can tell. I think we ordered them from the Dutch Label Shop because they have low lot minimums and very high quality personalization. They have a label wizard and default images you can get. We sew them into new clothes with a couple of stitches and pull them out when the clothes don't fit to reuse. But there are tons of companies out there who do this in our era of crafting searching in your favorite search tool for "Custom sew in labels" will return many hits.
Another option I've heard that's popular and easier than sew in (but not as removable) are the waterproof stickers made by many companies. We use them to label bottles and food containers but not clothes so I can't attest to that but an example of these is a company called "Sticker you". The sample images all have them stuck to the care labels in clothes which is great for clothes that have them but a lot of kids' shirts are going to printed instructions directly in the collar but you can probably still use these directly on the fabric, though it will make it stiff where it's stuck. Again, there are lots of companies who make these, this is one example that I've not personally used.
My personal preference (which is why we went with it) is to use the sew-in tags because they're removable, so if you give the clothes to a friend/family member, the name is gone... it's difficult to remove the stickers and the permanent marker. If your kiddo has sensitive skin, you probably want to go with the marker and learn to write small. We do use marker for small things that you don't want to sew a label into, like socks/hats.
We use iron on labels. They end up flush with the fabric so they're not too annoying (our oldest is quite sensitive to such things). They're quick to apply and are still quite difficult to peel off after two years of use. I've never had any come off on its own.