I use a different word depending on the manner in which I use the data. If I have found the made-up dataset lying around and have pointed my algorithm at it in a confirmatory manner, then the word "synthetic" is fine.
However, oftentimes whenever I use this type of data, I have invented the data with the specific intent of showing off the capabilities of my algorithm. In other words, I invented data for the specific purpose of getting "good results". In such circumstances, I am fond of the term "contrived" along with an explanation of my expectations for the data. This is because I don't want anyone to make the mistake of thinking that I pointed my algorithm at some arbitrary synthetic dataset I found lying around and it really worked out well. If I have cherry-picked data (to the point of actually making it up) specifically to make my algorithm work out well, I say so. This is because such results provide evidence that my algorithm can work out well, but provide only very weak evidence that one might expect the algorithm to work out well in general. The word "contrived" really sums up nicely the fact that I have chosen the data with "good results" in mind, a priori.
"does that give the impression of fraudulent data?"
No, but, it is important to be clear about the source of any dataset and your a priori expectations as the experimenter when reporting your results on any dataset. The term "fraud" explicitly includes an aspect of having covered something up or having outright lied. The #1 way to avoid commission of fraud in science is to simply be honest and forthright about the nature of your data and your expectations. In other words, if your data are fabricated and you fail to say as much in any way, and there is some kind of expectation that the data are not fabricated or, worse, you claim that the data are gathered in some non-fabricated sort of way, then that is "fraud". Don't do that thing. If you want to use some synonym for the term "fabricated" that "sounds better", such as "synthetic", nobody will fault you, but at the same time I don't think that anyone will notice the difference except for you.
A side note:
Less obvious are circumstances where one claims to have had a priori expectations that are actually post hoc explanations. This is also fraudulent analysis of data.
There is a danger of this when one chooses data specifically with the intent of "showing off" the capabilities of an algorithm, which is frequently the case with synthetic data.
To be clear about why this is the case, consider that the "normal" scientific method works something like so: 1) A population $D$ is chosen 2) A hypothesis $H$ is concieved 3) $H$ is tested against $D$ (or some sample chosen from $D$). Science doesn't have to work within this narrow definition, but this is what is called "confirmatory" analysis, and is generally considered the strongest form of evidence one can provide. Since the order of events correlates with the strength of evidence, it is important to specifically document them.
Notably, in the case of "contrived" data, the process often works more like so: 1) A hypothesis $H$ is conceived, 2) A population $D$ is chosen, 3) $H$ is tested against $D$. If you are testing an algorithm, for example, then the hypothesis that your fancy new algorithm "does a good job" might occur prior to the invention of the synthetic dataset. If this is the case, you should mention it. At the very least you should not purport that events transpired in a "confirmatory" manner, because that would lead readers to conclude that your evidence is stronger than it actually is.
There is no problem with doing this, so long as you are honest and forthright about what you have done. If you have gone through pains to create a dataset that gives "good results", do say so. As long as you let the reader know the steps that you have taken in your data analysis, they have the information necessary to effectively weigh the evidence for or against your hypotheses. When you are not honest or are not forthright, then this may give the impression that your evidence is stronger than it really is. When you are KNOWINGLY less than honest and forthright for the sake of making your evidence seem stronger than it really is, then that is, indeed, fraudulent.
In any case, this is why I prefer the term "contrived" for such datasets, along with a short explanation that they are, indeed, chosen with a hypothesis in mind. "Contrived" conveys the sense that not only did I create a synthetic dataset, but I did so with particular intentions that reflect the fact that my hypothesis was already in place before the creation of my dataset.
To illustrate by an example: You create an algorithm for analysis of arbitrary time-series. You hypothesize that this algorithm will give "good results" when pointed at time-series. Consider, now, the following two possibilities:
1) You create some synthetic data that looks like the sort of thing that you expect your algorithm to perform well on. You analyze this data and the algorithm performs well. 2) You grab some synthetic datasets because they are available why not. You analyze this data and the algorithm performs well. Which of these two circumstances provides the better evidence that your algorithm performs well on arbitrary time-series? Clearly, it is option 2. However, it might be easy to report in either option 1 or option 2 that "we applied algorithm $A$ to synthetic dataset $D$. Results are shown in Figure $x.y$." In the absence of any context, a reader might reasonably assume that these results are confirmatory (option 2), when, in the case of option 1, they are not. The reader has therefore, in option 1, been given the impression that the evidence is stronger than it really is.
tl;dr
Use whatever term you like, "synthetic", "contrived", "fabricated", "fictitious". However, the term that you use is insufficient to ensure that your results are not misleading. Ensure that you are clear in your report about how the data came about, including your expectations for the data and the reasons why you chose the data that you chose.
