A sprinkler head that is mounted in an inverted position is called:

The term for a sprinkler head that is mounted in an inverted position is indeed identified as a "flush pendant" sprinkler head. This specific type of sprinkler head is designed to provide adequate coverage while minimizing the aesthetic impact by being flush with the ceiling.

Inverted or flush mounting is beneficial in preventing obstructions in areas where headroom is a concern and ensures that the sprinkler functions properly without being affected by furniture or other installations below it.

The other options mentioned are also specific types of sprinkler heads, but they are not described as inverted. For instance, "pendent" refers to a type of sprinkler head that hangs down from a surface, designed for standard ceiling applications, while "conventional" can refer to traditional mounting methods without the specificity of being inverted. Therefore, while multiple types of sprinklers are acknowledged, the specificity of "flush pendant" is what makes it the clear answer for this question regarding inverted installation.