@ahmadhanb's answer is a good workaround but here is another way to deal with long tables.
Although there is no way to transpose a table in the composer, you can split your table into multiple frames. Now depending on the case, this could be more or less elegant, but this is how the result looks like:
Here's how to do it:
- Add a table as you would normally do and select its source layer.
- Scroll down the properties till you get to Frames.
- Click Add Frame.
- Align and resize your frames as may be suitable to your map layout.
- It is also a good idea to turn on Show only features visible within a map. This way you won't have a table with all the layer features on your map!
P.S. It is possible to rotate the table, but unfortunately, the text also rotates and you end up with vertical text, which doesn't look very elegant.