As you would expect, lots of their competitors have "smile" in their names. So instead, the name SmartMouth makes you smile.
Using the word "smile" in a name is explanative, using words that cause your audience to smile is demonstrative.
In naming & branding, as in all aspects of life, demonstrating is always more effective than explaining.
It's also a twist on a descriptive name, saying "It's a Smart choice for your Mouth" and that the dentist is "Smart about Mouths".
Since parents, not kids are the audience, giving them a laugh about their kids makes it work, makes it warm - and unforgettable.