What is the name of this tree?
This is a Crapemyrtle. They bloom in many colors (and are one of the latest to 'wake up' and leaf out in the spring.
They also come in many sizes and growth forms, from just a couple of feet to thirty feet, so choose carefully based on what the area where you with to plant can manage once it matures.
They often have problems with powdery mildew and cold hardiness in our area, so consider choosing one of the named varieties introduced by the U.S. National Arboretum which have improved disease resistance and winter hardiness.
Take a look here (there is a photo gallery as well):