I'm currently in the process of developing a counting application for preschool-age children. My client wants the child to log in by tapping his/her name on the screen. I have a great voice actor on my staff who has already helped with the other parts of the app.
This may be different now, but when I was researching elementary-level behavior a few years ago, it was standard to assume children would start reading in the 1st grade.
Pre-school is typically 2 to 4 years old, right? That may a bit early to require being able to read their name and know to tap it. I might do some recon with some 3 years old just to verify.
If I'm wrong, then having a voice prompt, such as "Press your name" or "what's your name?", might be sufficient.
Is this a web or mobile app?
If they aren't yet reading age, then perhaps a voice recognition element could be added. After a "What's your name?" or "Say your name" voice prompt, the child could say their name (which should possible for the majority of children at that age) and the system could recognize it and continue on - possibly even spelling it out loud for them.
Why does it have to be a name? If you can get a photo of each of them, which seems like a pretty simple thing today, just have them tap on their own photo. If you need to prevent error, when the child taps their image, the app could say "Are you Ellen?" and the child could tap on a thumbs-up or thumbs-down image or say "Yes!"