Can the use of a VPN be traced back to me?

If I use a VPN my college's school Wi-Fi, can it be traced back to me? Apparently it's breaking school rules to use one and I won't be using it again but if they know somebody's used a vpn can they find out who? It's on my iPhone X, I'm just wondering if they see my name or anything. I'm not doing anything bad on the school Wi-Fi, it's just that you can't listen to music or watch educational YouTube so when I run out of data sometimes I'll turn on this vpn on my phone to listen to music or do normal school stuff that's blocked for some reason.

They can track MAC addresses and identify the device used.

In the end, everything can be traced back to you - VPN, proxy or none.

They can absolutely trace it back to you. You are connecting to their network, and they can see your device (and the name you gave the device) and a stream of VPN activity.

Its very likely that they will simply ban your device from the school Wi-Fi

It really depends. If they just distribute a basic Wi-Fi password that everyone in the school uses then it would be difficult (not impossible) for them to figure out who owns the iPhone violating their rules, more likely you would just suddenly find your phone banned and then if you went in for help they would know. If you ever had to log into a kind of a web portal to enable Wi-Fi access for the first time they would know exactly who did it. Regardless colleges do not have time to pull everyone in the office for every minor violation. Some VPN's are also extremely hard to detect among 100's of users unless they start pulling a ton of bandwidth. They will focus on serial abusers, high bandwidth users, and those doing anything that could be illegal. If your phone still has access I wouldn't worry about it.

Well yes, they can tell who was on their network at any given time and what services were in use, most VPNs use specific non standad ports so can be picked out of the noise on the network. If they really want to they can trace back to you that you were using one, but not what you were doing or where you have been.

In some cases, NO. I use Nord VPN. I have a friend that is a Certified IT Tech at my ISP and he said if you had Nord set up correctly, that they could not see where I went. All they could see was that I was logged into my account. Of course, you need to have your Router/Modem set up correctly also.