I want to make name plates for my grandchildren out of pennies-Ideas?

Depending on what size you are looking to make craft stores sell wood letters already to decorate.

https://www.google.com/search?q=name+plates+using+pennies&biw=1002&bih=476&tbm=isch&tbo=u&source=univ&sa=X&ved=0ahUKEwiyluiC_9bRAhVM6IMKHQDKBwkQsAQIGQ

You can get mosaic metal forms of different sizes from an art supply store Hobby Lobby and the what is used to glue mosaic items to the inside then grout to fill in cracks. You can color the grout or get grout that is colored from home depot. This way you can use the pennies. Sounds like a very nice project.

How about covering wood letter blocks with pennies like this Hometalker- http://www.hometalk.com/diy/the-crafted-sparrow-loose-change-1858459

I like the idea of using a picture frame as the backing for the name plates; then you could decorate each picture themed for each child and them put their names in the coins on the glass. Using 8x10 size landscape would give more room for the names; if you have longer names you could go up to 11x17 or buy frames that are long and skinny.... or make them yourself.