General Instruction of the Liturgy of the Hours 93-98 describes the particulars of how to combine Mass with one of the Hours. Mass may be "more closely joined" with Evening Prayer, Morning Prayer, or one of the Daytime hours. Except for the option of an extended vigil of Christmas Eve that includes the Mass in nocte, Mass can't ordinarily be combined with the Office of Readings. The GILH doesn't even address the idea of combining Mass with Night Prayer.
Even though I've been going to Mass for almost nineteen years, and have been saying at least some of the Hours for seventeen, I had not experienced this liturgical option until very recently.
It's curious, or at least it is to me, that the liturgical services that result from the 'more close joining' of Mass with one of the Hours do not seem to have their own names. Our friars sometimes use the general term 'Prass,' a contraction of 'Prayer and Mass.'
Playing around with this on Twitter yesterday, I learned some other names:
Evening Prayer combined with Mass is called "Masspers."
Morning Prayer combined with Mass is called "Mauds."
I still don't know what Mid-Morning, Midday, or Mid-Afternoon Prayer are called when combined with Mass. Perhaps Tass, Sass, and Nass, or Merce, Mext, and Mone? I'm not sure about those.
Thanks to @caesius and @mikewgossett