I can't find airdropped on my iphone

Thank you so much for your help. This is a great piece of information to have. I tried airdropping a pdf file to my iPhone, but since I own both the laptop and the phone, the phone did not ask me to confirm the airdrop OR choose where to keep it. It did chime a signal, indicating the the airdrop was completed - but I could not find the pdf in my pdf app, or files, or photos - so I didn't know where to find it. Searching by name was a strategy I thought of, but couldn't figure out how to do it. A lot of online advice described using the Safari address space to search the name, but that didn't work. Your information was very helpful. Unfortunately, searching for the file using that method still did not show me the file on my phone, which is confusing because of the signal I got saying the airdrop was completed. I tried airdropping it three times, and the phone signaled three times, so I'm not sure if it really is on the phone and I can't find it, or if the airdrop signal did NOT indicate the airdrop was completed. Hoping I don't have hidden files filling up my storage, but at least I now know a method for searching for files on my iPhone. Thanks!