Hopefully, you don't work in H.R., or anywhere else where people are hired and laws need to be followed.
People seem to want to hire coaches based on name recognition. That sounds good at the time the hire is made, but as L268 says, that will fade quickly in importance. Laura Schuler's name is known to more recruits, but her name recognition isn't always a positive. Northeastern wasn't heading in a good direction when she stepped down, and UMD's recruiting wasn't exactly trending upward while she was there. All three have enough of a coaching resume that their playing resumes are basically meaningless at this point. None of us know what vision for the Minnesota State program each of the candidates has or ideas as to how to execute that plan. Those making the hire should, and they can get a sense from an interview and the coach's track record how likely it is that those goals are achievable. Mark Johnson is still coaching at Wisconsin not because he was on the '80 Olympic team, but because he could coach and demonstrated success in Madison before the movie "Miracle" came out and a new generation learned his history. People like John Harrington and Jennie Potter will succeed or fail because they can recruit, teach hockey, and get players to work for them; owning a gold medal will become insignificant in a hurry.
I've only heard good things about Amber Fryklund as a coach and has been recruiting the same pool of recruits for many years, so unless someone has a reason based on something other than his/her own ignorance, I wouldn't be so quick to dismiss her from the equation.