Swift/iOS: Subclassing UILabel and setting properties
You are using IconLabel to act as a container, it contains another UILabel and UIImageView. There is no need that IconLabel should be a UILabel you can just have your label nameLabel and your imageView icon in a UIView container. It means that you need to change :

class IconLabel: UILabel {

to something like

class IconLabelView: UIView {

another note, to keep your custom view generic it's better that you setup the background color outside the class like : 

let customView = IconLabelView()
customView.backgroundColor = Theme.supportLightGrayColor


also I think it's better to have two methods for the subview setup and constraints instead of one:

private func addSubviews()

and 

private func addConstraints()