I used to teach 3 years old in preschool.
Your son is off to a great start just because he has a mom that is aware and trying to help him. Don't worry about it. Every child learns at a different pace. I have had kids that were brilliant and could write their name perfectly at this age as well as other things. I have had kids that had no clue how to write their name, much less any other letters.
The first thing my kids learned at school was to write a whole page of lines. We did squiggly lines, straight lines, vertical lines, horizontal lines. Get it? LOL They have to learn how to hold the pencil correctly, how to control it and how to not get frustrated because their lines are not perfect. They also don't need to get burned out on learning before they get to kindergarten. Learning should be an adventure for them! ;-)
fwiw my youngest (and here I was teaching school) child of my own would not write his name at this age. He barely showed interest. At 4 years old he wrote his name if the teacher told him too, but had no interest in writing that silly alphabet. Then when he got to kindergarten I had him tested. The tester actually came out to talk to me. He said the kid's IQ was way up there and kept asking me about his preschool years. I told him I teach and all I could say was he must absorb it, but not want to show it. LOL When he got about halfway through Kindergarten he loved his teacher and just wanted to please her and show off so he started 'performing'. He was writing sentences and taking spelling tests by the time he graduated kindergarten. btw his birthday is June 30th and I did not hold him back so he is the youngest in his class.
So all that to say, don't sweat it. Have fun, show him something new every week, and when he gets ready he will astound you! ;-)
ts