There's nothing wrong with getting someone's name first.
If you have more than 1 plan, then you can answer the "cost question" by saying "we have different plans. What are you interested in?".

This question is usually asked upfront by people interested in going to the cheapest place. They're not going to pay extra because you are a 10th Dan Soke or you teach Karate instead of Tae Kwon Do. If there is something more important to them than cost they will ask that first.

Some may call and ask "how long does it take to get a black belt?" then ask either "how much does it cost?" or "Are you a black belt? What rank". If the rank of the instructor i smore important to them they will ask that. Again, they may very likely be interested in only going to the closest school and cost, style, teachers rank, etc mean nothing to them.

When I was training directly with my teacher I gkadly drove 40 miles past dozens and dozens of schools and there were another dozen or more closer in the other direction. But I wanted something specific. So I never called and asked "how much?". etc. It didn't matter.
But this is the way of thinking of only 2% of those who train in martial arts. The other 98% want fun at the closest and cheapest place.

One of the original answers was "are you a teacher or a salesman?". The teacher answers the questions and spends as little time on the phone as possible. The salesman tries to be slick and keeps the caller on the phone until they sell something.

So really, the answer to the qoriginal question depends on the goal of the dojo operator.

Are you looking for serious, committed students? Or are you looking for people who need a cheap place to drop the kids off for few hours a week and maybe people who are going to spend the nesxt 3 months at place that's on the way home from work where they can exercise.

I personally wouldn't trust someone who was too afraid to just tell me the cost if that's what I ask. It's a straigh forward simple answer. But sadly, what we are seeing in the Mcdojo industry is "charge what you can get". When someone is afraid toi just tell me "class is $80 month", I start to think maybe they are just trying to see how much they can get from me.

I had one student here who came over from one of the local mcdojo. He was in an "instructor training program". Part of the training was to figure out how much you can screw each person out of. There was no set monthly fee. If they drove up in a nice car and had nice clothes, it was one price. If maybe they looked more working class and on a tight budget they offered a plan. For a place like this they would be afraid to set a price over the phone. They would be disappointed if they told you $70/month and then you pulled up in a Mercedes and they realized they could have gotten a $100.

Reputable people, regardless of thier business, are not afraid to set prices and quote them over the phone.