Consider this . . .
Most design firms have a website or social media page where you can see the majority of their work. Make sure you look at as much of it as you can, and get familiar with their work. If you want a traditional home and you find a designer that almost exclusively does modern style homes, you probably shouldn't consider them for your project. You want to set yourself and the designer up for success, look for someone who has done work on projects similar to what you are looking for. If you want something that no one is doing like a Passivhaus, find someone that is willing to put in the work to learn as much about it during the process and make your project a success.
The interview process is important because it helps you get to know your potential designer. Whether you are looking for someone to build your brand new home or help with a commercial renovation you will spend more time with these people that you would think. You want to make sure that you get along well, trust their opinion, and can communicate accurately with them.
Make sure they actually listen to what you are saying or asking for, if you leave the interview feeling like they are just going to do what they want without consideration of your preferences or budget you should run away. Make sure they are willing to work with you to stay on budget
Who will be working with me?
Often your initial meeting isn't with the actual designer or design you will be working with during your project. It's a good idea to meet that person before you make your final decision so you know you like them too.
when can you start?
Sometimes a firm will have a little bit of a wait before they can even start the preliminary phases of a project. This is only a problem if you need to start right away. Many times people start looking for an architect before they absolutely need one so there is usually some flex time. If you are not one of those people and you need to start right away this basically takes them out of the running for your project, unless you like them so much you are willing to postpone your project for them.
is my budget realistic?
They understand you might only have a certain amount for your project, but sometimes what you want is just not possible for that amount. You will not be able to remodel and entire kitchen, living room and master suite for $20,000. Ask your potential designer if they think your have a realistic budget, see what they say and compare it to what the others say. If one says "absolutely not" and another says "it's not the ideal budget but I think with some careful material selections we can make it work" then you have eliminated one of the potential architects.
how will you help me stay in my budget?
Make sure they can help you select budget friendly materials, or if they can value engineer if the project bids come in higher than you expected. If they have experience with projects similar to yours they should have a general idea of cost per sq ft once you are into the design phase. On the other had, they can only do this as much as you will let them. If you have to have really nice (expensive) plumbing fixtures, and flooring, and light fixtures they can't just eliminate other things to accommodate your expensive preferences. If you have a budget pick the couple things that are really important to you and see if they can help you make it work. You can have anything you want, you just can't have everything you want.