Spiderwort
The name may not be attractive but the plant certainly is.
This is a small to medium-sized plant used mostly to add some lush green foliage to your garden. The rich blue and purple flowers are a bonus. Some varieties may have pink, white or red flowers but the blues and purples are most common.
The 3-petal flowers are unusual in their shape. They also seem to grow directly from the ends of the leaves rather than from a separate flower stalk.
They bloom in the morning during the summer and the foliage looks somewhat like a lush ornamental grass. It grows as a clump so it could look nice along a border.
Your spiderworts can grow quickly under good conditions so they can be divided every few years.