This is one of the Daiquiri series, just the frozen version. You should add a generous amount of ice to Frozen Daiquiri (because otherwise it wouldnt' be that frozen). It is supposed to be blended, thus its texture resembles a nice smoothie drink. If you want to experiment with the flavours and colours, you can add some fruity syrups to it, such as strawberry, cranberry, etc. In bars there are usually special devices that create a smoothie texture, but it is also possible at home just with a bit more effort. It is possible to get such an effect not only by blending the ice but also using frozen Limeade - a concentrated drink with the strong lime flavour. This will help you create the smooth texture and add both sweetness and sourness to the drink.
There are some romantic verstions to the Frozen Daiquiri, such as the Old Rose Daiquiri (add some rum and strawberry syrup) and the Daiquiri Mulata (takes a splash of coffee liqueur added).