My son had trouble learning to write his name because he never wanted to color which build kid's small muscles in their hands. I worked with him at home A LOT but I'm sure the teacher cant tell! Definatly let them copy it. let them trace it and get them to color, paint, use glue sticks, play with play dough, cut, use stickers, do puzzles, etc shaving cream, doing mazes, drawing lines from one thing to another, drawing circles, lines etc.
Write their names while they watch, then cut the name up, mix the letters and see if they can put it back together again-they can paste it. If this is hard then repeat every day!
Occupational therapist are now saying let them use little pencils (like golf pencils) not big pencils. Handwriting With Out Tears sells cool little colored pencils or crayons with two colors one on each side so the kids have to flip to change the colors. I often get students who come to kindergarten without preschool, without any experience with pencils, who cannot write their names( and dont recognize any letters) most do great because they are older. It really helps if they LIKE to draw and color and do art work and build those muscles. Its great your looking for the best way to help them!