Would this be a star cluster?

That’s actually a cluster of galaxies! You can tell they aren’t stars because of their extended elliptical shapes. For ground-based optical telescopes, stars are all way too tiny for us to see any structure – they just look like dots, but blurred out by the atmosphere. Galaxy clusters can usually be recognized by having lots of these smooth galaxies (not spirals), and they’re all basically the same color (with the color changing with redshift). You can sometimes confirm this by turning on the “SDSS Spectra” layer, where they have measured the redshifts to some objects. In this case, the central one, and one in the bottom-left both have redshifts about z=0.19.

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Is it possible to name a galaxy cluster?

It already has a name:
ACO 1602