Is water the most common multielemental compound?
You are indeed correct that the elemental molecule $\ce{H2}$ is the most abundant molecular species in the universe by far.[1]. In order to answer your question

Is water the most common multielemental compound?

I only focus on neutral species, of which around $50\%$ are in molecular, i.e. multiatomic form.[2]
In this category, second only in total abundance to molecular hydrogen $\ce{H2}$ is carbon monoxide $\ce{CO}$.
This has become evident during the extensive work that has been conducted in the last few decades as large-scale $\ce{CO}$ surveys of the Milky Way galaxy and other galaxies have been performed, further corroborating $\ce{CO}$ as the second most abundant neutral species and technically[3] as most abundant interstellar compound.
To conclude, it might be interesting to realize how substantial the difference in mass is still between the two most abundant molecular species in interstellar space:[2]

Estimates of the galactic mass of $\ce{H2}$ and $\ce{CO}$ can now be given with reasonable accuracy $m(\ce{H2}) = 2 \cdot 10^9 \; M_\odot$, and $m(\ce{CO}) = 2 \cdot 10^6 \; M_\odot$.

So in order to estimate $m(\ce{H2})$ which constitutes the bulk of the gas mass, carbon monoxide $\ce{CO}$ is typically used as tracer or proxy for $\ce{H2}$, as further reading I suggest a very informative post on the physics.SE: Why is $\ce{CO}$ a good tracer for $\ce{H2}$? How are those molecules correlated?
The mass unit $M_\odot$ is commonly used in astrophysics and represents the mass of the Sun, i.e. $M_\odot \cong \pu{1.98E30 kg}$.
The water molecule $\ce{H2O}$ is probably next, i.e. in third place, of the most abundant molecular (neutral) species in the universe which can be directly underpinned by the fact that it made up of the first and third most abundant elements in the universe, hydrogen $\ce{H}$ and oxygen $\ce{O}$*[4]. But I am not aware of any reputable source that explicitly states or confirms this assumption.
Footnotes &amp; References

vide, e.g. Why is $\ce{CO}$ a good tracer for $\ce{H2}$? How are those molecules correlated? or Wikipedia: List of interstellar and circumstellar molecules respectively

Winnewisser, G. The chemistry of interstellar molecules. Topics in Current Chemistry,Cosmo- and Geochemistry 1981, 39–71. DOI: 10.1007/3-540-10920-X_14.

vide ut supra, comment by Karsten Theis:

$\ce{H2}$ is not a compound, it is an element. It is a molecule rather than an atom, though.


van Dishoeck, E. F.; Herbst, E.; Neufeld, D. A. Interstellar Water Chemistry: From Laboratory to Observations. Chem. Rev. 2013, 113 (12), 9043–9085. DOI: 10.1021/cr4003177.