@Pascal's comment links to two possible solutions, but the bottom line is that you need to add the car names manually.
To know which car names to use takes a first step: if you look at mtcars, you'll see that they don't appear under a column header, meaning they are the row names. To get at them, simply:
carnames <- rownames(fourcyl)[ order(fourcyl$mpg, decreasing=TRUE) ]
From here, you need to know how and where to add them. Perhaps the first place many people look is to axis, where you'd do something like:
axis(side=1, at=1:length(carnames), labels=carnames)
But you'd be disappointed on at least two accounts: first, you don't see all of the names, since axis courteously ensures they don't overlap by omitting some; second, the ones that do show are not aligned properly under the corresponding vertical bar.
To fix the first, you can try rotating the text. You could use las (see help(par)) and do something like:
axis(side=1, at=1:length(carnames), labels=carnames, las=2)
But again you'll be a little disappointed in that many of the names will run over the default bottom margin (and disappear). You can fix with this a preceding par(mar=...) (again, see the help there and play with it some to find the right parameters), but there are solutions that provide slightly better methods (aesthetically), two of which are mentioned in @Pascal's link (really, go there).
The other problem -- where to put the labels -- is resolved by reading help(barplot) and noticing that the return value from barplot(...) is a matrix providing the mid-point of each of the bars. Odd, perhaps, but it is what it is (and it has a good reason, somewhere). So, capture this and you'll be nearly home-free:
bp <- barplot(fourcyl$mpg[order(fourcyl$mpg, decreasing = TRUE)],
horiz=FALSE, ylab = "Miles per Gallon",
main = "Efficiency for 4 cylinder vehicles",
ylim = c(0,35))
Now, to copy one of the link's suggestions, try:
text(x=bp[,1], y=-1, adj=c(1, 1), carnames, cex=0.8, srt=45, xpd=TRUE)
(No need for the axis command, just bp <- barplot(...), carnames <- ..., and text(...).)