Does the Sun have a numerical designation in any star catalogues?
It's somewhat difficult to prove it either way given the large number of catalogues out there. The majority (at least of the ones on VizieR) do not include the Sun.
The only case I'm aware of that almost meets your requirements is in the Preliminary Version of the Third Catalogue of Nearby Stars by Gliese and Jahreiß (1991). This catalogue is well-known as the source of stellar designations beginning &quot;Gliese&quot; and &quot;GJ&quot;, and is queryable via VizieR.
The first record in the catalogue is the Sun, which includes its spectral type, apparent magnitude, colour indices and space velocity as for other stars. Right ascension, declination and proper motion aren't included for obvious reasons. It doesn't match your requirement for having a numerical designation because the name field is just &quot;Sun&quot;, while the other stars in the catalogue have numbers. The &quot;NN&quot; stars originally didn't have numbers either but these were added in 1997: in the literature these objects are still typically referred to as &quot;GJ ####&quot; rather than &quot;NN ####&quot;.