Mint is a great name agreed but what's the actual impact? 5%? 10%? 50%? Possibly not even 5%
Impossible to measure that, because you can't do controlled experiments. But if you're asking, "Why did Mint make the first blockbuster web-based personal finance product?" I think you'd have to have their name/branding in the top 3-5 reasons.
Edit: But if you put a gun to my head and demand that I guess - then 35%. Totally arbitrary, but that's: The increased signup/conversion rate, increased trust, increased media/PR, increased word of mouth, and increased prestige/exposure/desirability for acquisition. I think it produces huge benefits in all of those areas.
The name might and does have some advantages, especially if it is short and relatively easy to remember, but the 35% should possibly go towards the two things mentioned, that is design, and user experience in filling in the form, 20% possibly marketing and the name would at best have a 5% effect.