Are there any naming conventions for heights (orthometric / above ellipsoid)?

Question

We are used to lat and lon names for describing latitude and longitude on the WGS84 ellipsoid. But I cannot figure out a single convention for naming the ellipsoidal height. The most common way of describing it is by the lower case h letter, e.g. on the geoid wikipedia page:

but it may be confusing to use a single letter and we may find other ways* of naming it.

Do you know any official (geodesy) document setting up a convention for naming heights, especially for the orthometric height (usual altitudes) and ellipsoidal height?

*
https://support.pix4d.com/hc/en-us/articles/202559869-Orthometric-vs-ellipsoidal-height
https://fsims.faa.gov/wdocs/orders/8260_54a.htm
https://www.bluemarblegeo.com/knowledgebase/calculator-2020sp1/Ellipsoid_Height.htm
https://gis.stackexchange.com/a/157010/65370

Answer 1

Isn't confusing to use h and H. And if it is, it would be difficult to find a geodetic document that uses other names, because that is the convention.

I don't know what you mean by "official (geodesy) document", but if a fundamental book of the discipline can be considered an official document, you can look for: Heiskanen, W.A. and Moritz, H. (1967) Physical Geodesy. W.H. Freeman and Company, San Francisco.