Eh, relationships aren't that simple. Not that this is canon, but I could see Tomoko feeling like "Mokocchi" is a name only Yuu should use. Yuu is still... PROBABLY her best and dearest friend, and so she gets some privileges. She's known Tomoko the longest and so on.
Of course she contacted Yuu rather than Asuka. It may be the case that Tomoko called Yuu first, also, rather than being messaged as Asuka messaged her. Asuka is definitely jealous, but she doesn't actually know who Yuu is to Tomoko (/slash doesn't remember seeing her picture).