The formula $a^2+b^2 = c^2$ is common knowledge and the words for hypotenuse and leg (is "cathetus" not used in English?) are basic mathematical vocabulary. Including these seems a good idea.
Connections to other mathematics
The notation with AB, CA and BC might be something the students have used or will use in less analytical geometry. Maybe you have an opportunity to mention that other context or tie these together, now or in a geometrical context.
Using some formulation without too much jargon is recommended; all the variables might be as much nonsense for some pupils, so this speaks for including some formulation that uses more natural language. This would also give you the opportunity to discuss why we use letters as variables in place of words (note that this is commonly not done in programming, for example; mathematics is peculiar here and an explanation might be order).
This also suggests avoiding needlessly difficult notation like subscripts, unless you feel that the students could use practice there and are ready for it, and would not have too much difficulty with Pythagoras. All extra cognitive load makes learning the main subject harder.
Conflicts in notation
As mentioned Chris in his answer, $h$ already has a different meaning in the same context, so you might want to avoid this. Think backwards and forwards to see if there are other unfortunate notational conflicts.
What does the curriculum that binds you say, if anything? Or maybe some other relevant guidelines. They probably don't go into this much detail.
What does research say?
You might want to a quick literature search on for example Semantic scholar (or other academic search engine of your choice), search for something like "pythagorean theorem didactic", pick the first few articles that are accessible and seem relevant, skim through them and check if they discuss the matter of notation or link to something that discusses it. It is very possible to not find relevant stuff right away, but worth a few minutes, at least.
You can spend as much or as little time as you want on this, but at least skimming an article or two might also give other ideas on your teaching, so why not?
In the end...
You have to check how much time you have and what the most important concerns for your students in the situation you are in. You can't do everything.