Can you actually name this number without looking in a dictionary? I cannot. Nine and a half zillions, I guess. So Alpha Centauri is like 44 zillion meters away; very enlightening.
Sure: nine quadrillion, four hundred and sixty trillion, five hundred and twenty-eight billion, four hundred million.
Next would be quintillion, sextillion, septillion, nonillion, decilion, undecilion, duodecillion, tredecillion...um...quaterdecillion(sp?)
Granted, I had to write it out to convert (or I could have sat and derived the rule--divide by three and subtract two to get the prefix). And I may be an exception, having spent a brief bit of my childhood interested in names for very large number. :-)
But it's pretty easy to know that 10^15 is bigger than 10^10. 10^5 times bigger. Ideally, we'd get sufficiently familiar with scientific notation to immediately understand that the difference between 9 lightyears and 9 000 lightyears is the same as between 10^12 meters and 10^15 meters.
I don't hold any illusions that people do have that fully internalized, of course. I don't.
You probably know Archimedes names for big numbers too :)
What I'm trying to say is that every sufficiently different field of human interest has some kind of units natural to this field. The metric system claims to be universal, but it's like one size fits all, but nobody looks their best. I can measure a backyard in millimeters, but why would I need it? I don't need this kind of precision there. A yard is a more natural scale because it's about the size of a step and this is about the right unit for what I do in the backyard. And inside the house I usually need a finer resolution, so I use feet instead of yards. If I build something on a smaller scale, I switch to inches; and so on. Every field has its best unit and the relationship between them is organic and is not always the fixed 1:10 as with metric.
You can always invent a name (and "light year" is nothing else, just not based on a "round" number of meters).
For example, since failure rates in safety engineering are usually pretty small and nobody wants to pronounce "something times ten to the minus eight" or similar, the term "fit" was invented to stand for 10^-9.
(Although I admit that "failure in time" is a stupid name for a dimensionless constant)
Similarly you could invent a "galactic length" or however you'd like to call it.
Light year is not just a name; year is a natural length of time and light speed is also a natural constant. The whole unit is natural and is based on things that make sense on such distances. This is same for all natural units; they grew up from usage. (This resulted in things that appears illogical, like having different with similar name for different applications, but this is only appearance. We measure water differently from oil or precious drugs and differently when we cook with water or build a dam, so it makes all the sense to have different units for different purposes.)
Meters, however, have a different story; the meter was invented by some French scientist about the time they were changing everything after the revolution, including month names; somehow month names reverted back to normal, but meters stayed. The meter was initially defined as 1/40,000,000 of the length of a meridian. Here only the length of the meridian is natural to some extent, although I fail to see how it is relevant to what is normally measured with meters, and the constant is completely artificial.