There are several species of black-eyed susan. Some varieties are annuals or biennials, but most are perennials. In general, seedheads are attractive after the petals fall and are usually left on the plant for winter interest. They also provide good food for the birds in the autumn and winter. Plants may seed to almost weedy proportions in some situations. If this is not desired, some or all of the seedheads should be cut down.
If just planted this season, they need to develop their root structure and become acclimated to your garden. This will happen over the winter.