I'm in freshman year college right now and I'm questioning whether my teacher is actually right for me. If you're studying with a teacher you know is a really good fit for you (and/or has produced many successful students), I'd love to hear why. What makes you feel confident that your teacher can actually help you get there?
Do they have a clear long-term plan for your development (e.g. preparing you for grad school/auditions)? Were they able to pinpoint your strengths and weaknesses right away? Do they actively suggest competitions, festivals, or other opportunities for you?
Basically - how do you know your teacher isn't just a big name, but actually the right guide for your future?
I had a great experience studying with an undergrad teacher (teacher 1) who very much knew what she was doing but was not a big name. She did all of the things that you list in your second paragraph, and found me a great instrument to play on for three years. She was a wonderful teacher, but I was far from a perfect player after leaving her class.
After this, I went to study with a very famous teacher (teacher 2) for grad school. This was a far more complicated and fraught relationship, but not bad or abusive, and I had relatively little success while I was there. But I listened to him, and what he taught me was effective, particularly in the year after I graduated when I had time to let his teaching sink in. I question that I would be competitive as a player in the long run without the tools that he offered.
Interestingly, I have a much more solid relationship with teacher 2 than teacher 1 these days and teacher 2 has been extremely supportive, kind, and believing in me since I stopped studying with him.
At school 2 I had a network of other faculty mentors, especially in chamber music, who offered unconditional support when teacher 2 seemed not to, and encouraged me to do things that teacher 2 would rule out for me. This is so critical if you have a sustainable but not optimal relationship with your teacher, because it enables you to actually learn something from them even if the relationship is not perfect.
These things are really complicated and I think questioning whether the fit is right is smart. But if you are considering switching/transferring I would have an honest conversation with your teacher, and think about the other parts of the school and whether losing those would be a plus or a minus for you.
Maybe it's worth thinking about what it is you want from your teacher, and whether or not your current teacher is/will be able to offer it? As someone who teaches in addition to my playing career, I always appreciate a student who comes in and says "this is what I want to be able to do that I can't do right now," or "my goal is X." Do you think this is something you could bring to your teacher, so that they can help guide you more toward what your actual goals are?
My best teachers more or less gave me the tools to solve problems through practice on my own (and offer some tips/hints/tricks/etc along the way, of course), which I've found invaluable now that I've been out of school playing professionally for about 10 years. A couple of them were "big names," but another was just an excellent teacher/mentor. I also had one teacher that I just...never fully got on with, so it happens.
Not sure what you play, or where you're in school, or who your teacher is, but maybe just being direct with them about what you want could help? I think that'd more or less be the deciding factor for me.