I'm a college student applying for an internship.
Until Monday, I was in the recruiting pipeline for 2 companies. Then, one of the companies extended an offer, which I accepted (for a summer internship). I notified the other company that I could not continue in the recruiting process for summer internships, but that I was available for jobs during the academic year. The company thanked me for letting them know, but that most likely the process would stop as they rarely offer non-summer internships. Also, they asked which company I will be joining for the summer.
Should I tell/am I allowed to tell them which company I'm joining? I have not signed any NDAs with my soon-to-be summer employer restricting what I can or cannot say; it's very common for students to post on the LinkedIn profiles that they are "incoming interns" at whatever firm they'll be joining. I'm just wondering if there's any nefarious motives here, or if my recruiter just wants this information for data collection purposes.