Rock climbing shoes are designed to be worn without socks, to have as little wiggle room and dead space in them as possible. Socks can cause your feet to slip and move around a little bit inside of the shoes, which could reduce your performance.
Most climbers don't wear socks with climbing shoes, but many do. If your shoes are a little bit too big, a thin pair of socks can help fill in that extra dead space. A thin pair of socks can also help reduce friction in new climbing shoes, which could help reduce blisters and other sore spots.
To mention rental shoes, while I have never worn rental shoes and will chose to never wear them if I have the choice due to not wanting to wear something so many sweaty and stinky feet have been in, socks could be a great choice. If you are like me and are more than slightly grossed out by rental shoes, wearing socks can give an nice extra layer between you and the shoes.
