You don't have to know skaters to ask them which coaches they think are good. Do it.
But good for one person isn't good for everyone. Individual learning styles are so different, that you have to watch them teach to see if you are happy with their teaching style, and whether their students of about your age and learning style seem to be learning. Do you learn best through demonstration, word descriptions, physics explanations, being physically guided through a motion, or through some combination? E.g., some coaches have a nearly perfect visual memory, and assume you do too. They only demo once. Some coaches know intuitively which muscles to use to do what, and assume you do too - and they don't know what muscles they are using, so can't tell you.
(The same issues exist with all teachers, in all subjects. Good teachers adapt.)
OTOH, you can give coaches guidance on what type of help you need to learn.
For me personally, the coach still has to be a good skater. I know this is completely unfair to coaches who are too old to skate well, but while words, muscle usage, and physics explanations are very important to me, I also need good demos. I am so unintuitive at athletics that I need coaches who are good at everything. Regretfully, such coaches don't usually come cheap.
I ran into a problem with an ice dance coach who had competed at high levels. He and his partner were encouraged to skate in a very distinctive style, a fact that gave them higher scores. But it made it hard for me to adapt to other partners. It would have made more sense to pick a coach with the same style
Coaches specialize somewhat too. E.g., Freestyle, Ice dance, Synchro, Pairs, Moves, and School Figures. some extent have different styles.
A lot of people take a few group lessons with many coaches, then pick the one whose teaching style they like best as their private coach. You might ask group lessons whether they are taking new private students of your age and talent level before taking their class.
I would ask any coach whether it is a problem for them if you occasionally go to another coach for help with something that you have trouble learning from them. Some coaches are very possessive
.
Don't ask the front desk. They either don't know, or they often play politics.