Trust yourself first before you trust anyone. Go on your gut and keep names and numbers safe.
A few times I have not kept numbers and when it came to getting my images, or following up with a photographer it was a nightmare.
Also sometimes when something goes well and you want to keep in touch and build a business relationship, or modeling venture, that could lead to more work, it is good to keep names and numbers handy.
Also you can use your email account as a great way to save addresses and notes, and letters which can be proof of the job, the date, and what was said.