Mine learnt to write their names in Nursery. YR built on that. I’m amazed you haven’t taught him to write his name at home before now. Especially if his pencil grip is ok. However school should have built on this. What does the curriculum look like? Have you seen it? What should he be able to do?
Prep schools vary. A lot. Some have everything. Some are fairly limited and are a bit of a refuge from the state sector! Where I live, the state sector is pretty good. Many state schools do have a wonderful range of activities and parents supplement this by paying for out of school activities such as extra sport. I’m glad my DD at state school didn’t have sports matches every week but she did have music tuition, orchestra, choir, and sports day was a serious affair! Lots of the DC did football, cross country and netball. Out of school she did piano, brownies, music centre string orchestra and choir, swimming and dance.
DD2 did go to a prep but we took her to tap, ballet and modern dance as extras. School did everything else. That was a top prep though and way above our local one which had very little sport, music, art etc and poor specialist facilities. DD2 went there for nursery and YR but it really wasn’t great above that. So we left for somewhere that had everything.
With the new assessment of DC, many state DC far exceed the NC requirements. No one talks about working years above the curriculum but greater depth is valued. Brilliant teachers can ensure this happens in the state sector. Few state kids would get to Oxbridge if they were not able to work beyond the curriculum. Plenty of state schools have very bright DC and teachers who know DC must make progress. They might even share the curriculum with you!!