Term for open-ended algorithms
Informally, you might call this lazy evaluation, or a lazily-evaluated stream.

A $O(f(n))$-time delay algorithm is guaranteed to output a stream of answers, with a delay of at most $O(f(n))$ time between answers.  One consequence is that outputting $k$ answers will take at most $O(k \times f(n))$ time -- but you also know that you won't ever have to wait too long for the next output.  (So, this helps rule out algorithms that return the first $n$ answers very rapidly and then take a really long time to return the $n+1$th answer).

An output-sensitive algorithm is an algorithm that outputs a stream of answers, and where the running time is some function of the length of the output.  Normally we evaluate the running time of an algorithm as a function of the length of the input, but an output-sensitive algorithm is analyzed in terms of the length of the output.  That's potentially relevant here.  Suppose your goal is to enumerate all fidgets in a warbuggle.  If you find an polynomial output-sensitive algorithm for this task, then you have an algorithm that's potentially useful for streaming purposes -- in particular, the average delay between outputs isn't too large (though the worst-case delay could potentially be quite high).

If neither of them captures exactly the concept you have in mind, then I suggest you just describe in text what properties your algorithm has, and don't worry too much about finding a short term for it.