The most common seal is a name seal, and the most common name seal contains both first and last names. Artists also use seals with just their last name or with just their first name. If you have a seal with your full name it will usually be used next to your signature. Most common is to stamp the seal directly under the signature, assuming you are writing Chinese in traditional style from top to bottom. There are no hard and fast rules though, so name seals may be found alongside a signature or even directly on top a of a signature. But a name seal is seldom used directly above the signature (I don’t know why). Name seals can also be used instead of a signature—artwork is often found with one or more seals but no signature, and seldom the other way around. The seal is like a stamp of approval indicating that the artist considers the work of art finished and worthy of their seal. A signed work of art without a seal may not be considered as valuable by the artist since, in imperial China, everyone learned to write by copying the calligraphy of recognized masters and so everyone was skilled at copying handwriting. For this reason a seal was thought of as a better proof of authenticity than a signature. When carving a seal the blade may slip in unexpected ways and the stone may chip unpredictably so that it was much more difficult to forge a seal. Of course, with modern technology that’s no longer the case.
The painting illustrated above is by Bada Shanren (1626-1705) and includes his signature over two seals (the bottom of the two is his name seal). There’s also a “corner seal” at the lower left and an inscription in the top right. Cover up any one of them and see how it changes the design.