From
https://voyager.jpl.nasa.gov/mission/did-you-know/ :
"Through the ages, astronomers have argued without agreeing on where the solar system ends. One opinion is that the boundary is where the Sun’s gravity no longer dominates – a point beyond the planets and beyond the Oort Cloud. This boundary is roughly about halfway to the nearest star, Proxima Centauri. Traveling at speeds of over 35,000 miles per hour, it will take the Voyagers nearly 40,000 years, and they will have traveled a distance of about two light years to reach this rather indistinct boundary."
So, about 80,000 years to reach the nearest star, if using the same method as Voyager. And that involved a "grand tour" of the giant planets to get multiple gravity assists.
The New Horizon probe only used Jupiter for its gravity assist, and was going about 24,000 mph when it went by Pluto.
So, yes, "We're gonna need a faster starship!" if we want to even send uncrewed probes to another star.
But, names of ships are fanciful, not deterministic. And we have to admit that "StarShip" is likely to get a lot farther than "StarLiner", even if both never get away from our star we have named "Sun".