First of all, let me set one thing straight: there is no one "right designer" that will be the perfect choice for any and all projects. There is, however, a right designer for you.
Some professions are very cut-and-dry about how you're supposed to serve certain duties. Accounting, for example, leaves very little room for creativity. Since design is equal parts strategy/know-how and creativity, you'll want to hire a designer whose creativity lines up with you. That can be a little intimidating, since there's no formula or accreditation you can look for that will guarantee that the designer you hire will do good work for you.
There may be no concrete ways to find out who the most qualified designer is, but there are methods that can help you find a designer that will create work you love in a professional manner.
The first thing you should be looking for in a designer is a portfolio that inspires you.
In the end, by hiring a designer, you want to get a beautiful and effective design of some sort - this is your first priority. So, when trying to choose a designer, the first thing you should do is find designers whose work you're drawn to.
There are a lot of ways to do this:
Search portfolio-based sites, such as Dribbble or Behance
Search freelancing sites, such as Upwork or Freelancer
Search "graphic design" or "logo design," etc on your favorite social media platform
Ask for suggestions from your fellow business owners and friends
If nothing else, this should give you an idea of what style of design speaks to you. Once you find a few designers that pique your interest, you should check their full body of work.
A good portfolio has:
Consistency of quality
Attention to detail
Range of techniques and/or clients
These three qualities tell you the designer can adjust to your specific needs and deliver consistently high-quality work.
Now that you've found some designers with talent, you should figure out which ones have good work ethics.
You should trust the designer you choose to work with.
Design matters, and design costs money - the last thing you want to do when hiring a designer is feel like you're going to get ripped off or taken advantage of. There are no guarantees in life, but there are two simple ways that can help you weed out the bad from the good:
Use social media
Talk to them
If the designer you're considering runs their own business or works freelance through a provider (such as Upwork) there should be testimonials and/or reviews from previous clients, and if there's not, that's a huge red flag. (It usually means they're hiding something, or have never had successful design jobs!) The more reviews a designer has, the better a feel you can get for their working methods and success rate.
Social media is a great method for figuring out the personality and ethics of the designer you're considering. If they're always complaining about work and clients on Twitter, that's a sign that they don't love what they do and won't give your project the care they should. Or their social media could show that they truly are passionate about design and their clients. You can learn a lot about a person from social media. (This could easily turn into a "careful about what you put online" article.)
But overall, the best way you can figure out how trustworthy a designer is is to talk to them! You don't even have to bring up your project right away, just ask questions about their working methods, how long they've been designing, or anything you're curious about regarding working with them. A lot of designers will even hop on Skype with you if you're more comfortable with that.
Don't let your uncertainty about the hiring process get in the way of your bigger business goals. Do your homework, and find a great designer to work with!