You are away from the Earth in one part of the universe and looking at a galaxy in another part of the universe, then which way is up? Does the universe (or near universe) have a celestial north? If you took a picture of that galaxy, then is there a correct orientation for displaying that photograph?
No. There is no prefered direction of the universe. The universe is homogenous and isotropic, on the large scale, to the best of our knowledge. This means that there is no "special" location in the universe, and no "special" direction.
There is, therefore, no "correct" orientation for the photograph.
Short answer, no, not like we do for the Earth and solar system.
Longer answer: kinda. The IAU has defined the International Celestial Reference Frame (ICRF). It is the coordinate system used to locate an object in the universe in as near a fixed coordinate system as we can define, based on very distant radio sources. A simplified defintion is the Z axis is aligned with where the Earth's North pole was pointing Jan 1 2000 00:00 UT1. The X axis point to the J2000 ra/dec coordinate 0,0. And the Y axis is perpendicular to both of those.
So this Z axis is the best definition for North or "up" we have.
The universe looks close to homogeneous and isotropic, but there are deviations and puzzles. The current puzzle is known as the axis of evil. Some features in the cosmic microwave background, along with a claimed pattern in the rotation axes of distant galaxies, appear to line up with the ecliptic (the plane of Earth's orbit around the Sun). Of course, all the data are taken from Earth or its vicinity, looking through the dust in the ecliptic. The ecliptic geometry also influences space-based observations: you need to look away from both the Earth and the Sun. So, perhaps, this is some sort of observational bias even though the folks who do this put a lot of effort into correcting for such biases.
A study of 200,000 galaxies shows a significant bias in their rotation direction, increasing with redshift, suggesting that the entire early universe was rotating.
Caveat: This was reported in popular media almost two years ago, and I haven't heard any updates.