In my game (https://technomancy.itch.io/bussard) I consulted star maps of nearby regions of the galaxy (http://www.projectrho.com/public_html/starmaps/mapindex.php) and placed systems accurately.

However, I felt that using their astronomical names/numbers would be unrealistic--if these stars ever ended up being colonized, they would be given colloquial names, so I made up my own names for most of them.