Every state has their own handwriting style that they teach. Most are quite similar, but there are silly little differences between them (I call them silly because I have moved interstate twice, and I think it could do dreadfult hings to a child's SE to be told that their style was wrong.
Schools generally show interest in whether or not a child can write their name; it's a reasonable indicator of where they're at, but it's not really a big deal if they can't. Some kids just aren't interested.

I've dealt with a few schools that insist children be able to write draw in pencil (not texta) as they develop the motor skills needed to control their writing implements better when they do this.

Names should be started with a capital letter, then the rest in lower case. It's how they're written/typed, so why start teaching any other way? But, they shouldn't be writing all in capitals. Lots of parents encourage it; capital letters have more straight lines so are perceived as being easier, but it's incorrect. Similarly, all text that children are exposed to should be printed correctly. I get on big soapbox rants when I see signage in kinders/c'cares that is all in caps, because it is such a bad example. The reason we don't write all in caps is that the eyes actually can't read it as fast, because all the letters are the same height and shapes aren't as easily differentiated.
So, um, maybe that doesn't answer your question. But I feel better for having ranted