Truthfully at 3 that is expecting a bit too much to hope that they can write it. When they go to kindy/school it is all taught there and they will be revisiting it all and can possibly get bored - my mum is a teacher and has seen this happen. Its fantastic if they can go to kindy learning how to write their name but it is in no way expected.

Starting to recognise letters is a good help for them - maybe start with the letters in their name and make it into fun rhyming games eg A is for apple etc. If you are adamant on teaching them how to write then you can buy books where they trace over letters and then erase them (like whiteboard type of pens)...I have found them helpful as you can resuse them a number of times.

Personally you will find that if you teach your children to love books and read to them heaps they will actually pick up on the letters and sounds really quickly when they start their formalised learning. I wouldn't be rushing them at this age, they have plenty more years ahead for that!