A different possibility in SU itself is to use a FlatText plugin (there are three - two free but limited, and one Pro, paid for but not expensive). This draws SU 3D text with no thickness but a small offset from the face you place it on, to prevent Z fighting if you give the text a fill. The text is editable after placement.
You can get them from the Extension Warehouse - search for FlatText.
I believe there’s another plugin by TIG or thomthom that makes 3d text editable, but I haven’t used it and can’t remember exactly what it’s called.
You can include the text in your component, and also assign it to a layer of your choice.
PS. SU label text automatically picks up the name of a labelled component. You could temporarily attach a label , copy the component name, and paste it in to FlatText, if the component name is a useful part of the label you want to add.
And if you can make a font character, you could include a small logo or vector image.