* Swirl: This is a general term for any curved or spiral design.
* Scroll: This often refers to a stylized scroll shape that is frequently used in decorative borders or as a decorative element in text.
* Flourish: This term describes a decorative element, often in the form of a stroke or series of strokes, that adds embellishment to text or a design.
Depending on the specific shape and context, the "swirly thing" could also be called a vignette, ornate design, or simply decoration.
To be more specific, please provide a description or image of the "swirly thing" you're referring to.