Your model will only do what it is trained for, regardless of what name your dataset(s) have.
Name of the dataset is just an organizational issue which does not go into training, does not really effect the amount of loss that will be produced during a training step. What will effect your models responses is however is the properties of the data.
Sometimes data from different datasets have different properties even though the datasets serve for the same purpose; like images with different illumination, background, resolution etc. That surely have an effect on the model performance. This is why mixing datasets should be performed with caution. You might find it useful to have a look at this paper.