Good morning,
My library is also thinking of running this program for this year's summer reading program. We are going to set up a mailbox in the library to avoid giving out personal information to other patrons. We will ask patrons when they register for our program whether they want to participate in this or not. Those who do want to participate, we will assign them someone random out of others who are also participating in the program.
Whenever they would like to drop off letters for their pen pals, they may do so using the library mailbox. Then, myself or another staff member will reach out to the pen pal and let them know there is a letter to pick up.
I wish you well in this endeavor - it's a super fun idea!