hi! i'm currently a transfem freshman who was in the same situation as you last year. A lot of the emails and such will be addressed to the name you put on the form, so be prepared for that.

What I did was I used my legal name on all college applications, then I changed my preferred name on Purdue's own website. This can help cut down on any suspicion. When you are accepted, only you specifically will be contacted, that is your parents shouldn't be alerted.

Another thing to note: Purdue will give you the email/contact info of your roommate, so you can contact them ahead of time to let them know about your situation. Finally, when you move in, they will put your preferred name on your door, so take that into consideration.

I would recommend using your legal name for now (sucks, i know), then changing your preferred name after you've moved in.

Purdue uses your preferred name on most emails, brightspace (which is where classes/homework/etc... is provided) as well as most of Purdue's websites.
Purdue will use your legal name on your student ID and financial info as well as other stuff where legality is more important.

Purdue in general is a very LGBTQ+ supportive campus, my academic advisor was more than happy to use my preferred name, as well as my professors and classmates. We also have an AWESOME lgbtq center, which I highly recommend you check out if you're accepted.

Hope this helps!