I separate the answer in three parts.
From a professional point of view, I would avoid offering graphic selection options to a client, as long as they are not firmly justified, reasoned and described in a guideline. My practical reasoning is that a client pays to get solutions to a problem.
...choose whatever orientation fits best into the context...
It looks you are transferring to the client the doubt you raise in this question. If I were the client at every moment I had to choose between one option and another I would have the feeling of making part of the work that designer hasn't done.
I know that this is not part of the question, I show it only as an add. There's a visual decompensation in the gaps. The pictogram bottom is too close to the text. Perceptively anchors the image to the typographic base. I'm not sure centering the pictogram to the text block is the best option in this case. In the image, the pink is as it is now and the cyan triangles are balanced after moving up the image a little.
A solution attempt is to balance the resultant gaps of the parallel virtual line that follows the alignment of the text and the right ellipse.
The result set free the image of the typographic block.
My personal choice would be to release it even more. Knowing that there is a deliberate and effective formal contrast, creating a dependency on the image with the text invalidate it.
From the conceptual point of view, when seeing the logo for the first time and before reading the question, at the first instance it is evident the pair of reflected ellipses that lead to interpret a winged insect. Immediately afterwards, two large sharp needles appear.
If the sequence is needles + wings, the association is inevitable.
If the sequence is wings + text, the result of the previous image is not so immediate. If this association is not done deliberately, I would try to:
- Avoid the sequence "needles + wings"
- Moving as far as possible any ellipse of the character that presents
a sharp needle to avoid any perceptual conflict: knife + balloon
- Place the visual weight of the image above the needle character tip