As already said, it is "Hasty generalization" as subset of the more enclosing "Faulty generalization". For the sake of the arguments below, I simply assume that the observation of data points was honestly acquired (no bias), but lack in observation size.
It must be said that it is not really a true/false fallacy. If you estimate the chances for false positives or false negatives with small sample size, you get very high chances that your conclusion is errornous. Hasty generalization over- oder underestimates the chances for being wrong, but in contrast to many fallacies it does not necessarily mean that the conclusion is actually wrong. So if several outcomes are in fact possible and your hasty generalization deduces one specific outcome, the generalization can be in fact true (!).
In fact many scientific discoveries by single persons which looked like measurement errors were in fact genuine (for example cosmic rays), but there are also important looking discoveries which turned out to be dupes (for example N-rays).
Anecdotal evidence is also not zero evidence, but weak evidence (!). Like the Sorites paradox, you cannot assign arbitrarily a 0% probability for an observation because then you never get a valid probability for a higher number of observations.
So the true problem is getting a valid estimate for the probability of the outcome. Let's say we e.g. want to explore an unknown tribe and we don't know anything about them except their existence and if they are friendly/hostile.
Now if the first meeting with one tribe member ends friendly/hostile, hasty generalization would come to the conclusion "The tribe is friendly/hostile" when in fact the likelihood is 50%. If we make more contacts, the calculated hostility will very fast converge to a good prediction how friendly/hostile the tribe really is.
The problem is not a small dataset in itself; if only a small dataset exists, it is not a fallacy to say: The probability of an error in our dataset is 24%. The fallacy is over- or underestimating the probability of an error severely.