In Jain cosmology, the next yuga/half-cycle will also have 24 Tirthankaras.

However, their names are not commonly given in the same way as the current 24 Tirthankaras of this avasarpiṇī. In Jain tradition, each time-cycle has its own set of 24 Tirthankaras.

So the clear answer is:

• Yes, there will be 24 Tirthankaras in the next yuga
• Their specific names are not generally emphasized in present Jain teaching

If you want, I can also list the 24 current Tirthankaras.