There is a reason why I really like the term "Rate limited Free Transactions" and the reason is that it contains only very simple words. As you have probably noticed

I am not a English native speaker. That gives me additional perspective, which I believe I share with most people on the world for which English is not a native language.
There is a great website
http://www.wordcount.org/ where you can check the rank of English words based on the frequency in which they are appear in a real language.
For example words from "Proof of Work" have ranks:
Proof - 3435
of - 2
Work - 103
So I consider term "Proof of Work" as quite simple.
What about "Rate Limited Free Transactions"?
Rate - 500
Limited - 984
Free - 449
Transactions - 4094
So... the worst rank in that case has a word "Transactions", which I think we cannot avoid to properly describe our feature. Besides "Transactions" worst rank is only 984.
What about "Transactions for shareholders"
Transactions - 4094
for - 12
shareholders - 3101
As you can see, shareholder is not a not very commonly use words. Besides... term "shareholders" is not very commonly used in cryptocurrency world. The reason for that is... because most of the world do not think about Bitcoin as a company. Of course Bitshares introduced DAC concept, but still it is not commonly used term.
How about Zero fee transactions?
In that case rank is:
Zero - 3895
Fee - 3251
Transactions - 4094
But the whole problem with that term is... that in my opinion it says nothing that you have to do something to have a possibility to make a free transactions (you have to have a stake)... or it not warns you that you that there is some limit for performing free transactions.
Perhaps something like "stake-weighted free transactions" would be more easily understood by most people.
This term is great in a describing how this actually is implemented. But in my opinion it is too technical.
Rank:
Stake - 4107
weighted - 1227
Free - 449
Transactions - 4094
and... I have no information about conjunctions of words "stake-weighted"
And.. in my opinion stake-weighted term stands to close to mathematical concept of "weighted arithmetic mean"... which I guess a lot of people heard of in school, but I think it was not the favourite thing on math lessons in school for most of the world

In summary:
"Rate Limited Free Transactions" for sure is not the best, but in my opinion it says a lot in a very simple way.