Honestly, there are many many threads on iterations of this question and they've all answered this question to death. At this point, there's nothing you can do about it because you're already set to matriculate and so there's no use worrying about it now. Best to put your best foot forward. But here's the longer answer.
Nobody on here likes to acknowledge that medicine isn't really a meritocracy. It is up to a certain point but then it depends on the same factors that other occupations and professions depend on, i.e. interpersonal skills. Which is code for networking and who you know. So let's break this down. First, I have to write the disclaimer that this is specialty-specific. If you're talking about specialties that are competitive or top academic programs in a certain specialty, then this applies. If you're talking about specialties that are not competitive, then this will not apply so much. Okay. So I split the advantage of medical school into categories - direct advantages and indirect advantages.
Let's start with direct advantages. This one is easier. A direct advantage is an advantage that is directly based on someone seeing your school name. In simpler terms, it's prestige. Prestige matters. You can see this from looking at any match list from the top schools. They tend to send their students to other top schools. Yes, part of it is that these students were all high-achieving in the first place and their advantage was just compounded by going to that school, but anybody who tells you that prestige doesn't matter is lying to you. That isn't to say it's the end all be all though. It's not. Think of it as a ladder. You're trying to get that competitive residency that you want. Being from a top school means you start off higher on the ladder. If you're from a not-top school, you're still on the ladder. You're just lower down. Doesn't mean that you can't make it. It just means that it's harder. But with hard work, it's possible.
Now that brings us to indirect advantages. These are things that are available to you during medical school that help you move up that ladder. People at top schools also have an advantage when it comes to this. There are more research opportunities at top schools and world-renowned faculty. You will likely be doing research with someone who is well known in the field, or at least you will meet them/work with them on rotations. This stuff matters for the competitive specialties. They're small specialties where somebody making a call for you can make a huge difference - even more of a difference than test scores. Simply put, there are just simply more opportunities, research and otherwise. At schools lower down, you as a student have to seek out those opportunities and be proactive. Again, it doesn't mean you can't get to the top rung with what you have. But you have to maximize what you have.