Send it only once for each child. As other children become school age, a letter can be sent to register them. Include the name, birthdate, and address of each child of school age. If you should move or stop homeschooling, you are required to send a similar letter of termination. Record keeping can be elaborate or quite simple.
Most people choose something in between.
As homeschoolers become older and more independent, it is often easier for them to record their activities themselves. A calendar can serve as a daily log, a notebook can be used to record books and reference materials, and a file box can hold samples of artwork, photos of projects, etc. We started out simple, but found we really enjoyed adding to our scrapbook. The Home Education Act calls for an annual evaluation of some kind. Many parents choose standardized testing.