What is the moon zenith called?

The time of day when the sun at its zenith, relative to the observer, is called "noon."

What is the lunar equivalent? "Moon's zenith" sounds so clunky.

Zenith, in its sense “(astronomy) The highest point in the sky reached by a celestial body”, actually is quite suitable for the purpose. In some sentences, lunar zenith may read slightly better than moon's zenith.

A term that is technically correct but may be misunderstood is transit, in its sense “(astronomy) The passage of a celestial body across the observer's meridian”. A problem with transit is that another sense, “The passage of a celestial body ... across the disk of a larger celestial body” is more-commonly associated with moons and satellites than is the meridian sense , which is often associated with stars. Thus, previously-mentioned culmination's sense “(astronomy) The attainment of the highest point of altitude reached by a heavenly body; passage across the meridian; transit” may be a better choice.

One can say zenith moon as a counterpart to noonday sun, although it is not nearly as common.

Note that the astronomical term zenith actually refers to the point directly overhead the observer, not the highest position a celestial object rises over the horizon, which would be its culmination.