The short answer is no—nothing automatically shows colleges how often a student took the SAT.
Most colleges let students who take the SAT multiple times select which of their test scores, by date, they send to colleges. However, some colleges do require applicants to send all their test scores.
Some colleges will look at the student's highest Math Test score from all test dates and combine it with the highest Evidence-Based Reading and Writing score, even if those scores are from different test dates. This is called superscoring.
You can find out a college's policy by checking its website or contacting the admission office.