How do I extract just the number from a named number (without the name)?

For a single element like this, use [[ rather than [. Compare:

coefficients(out)["newx"]
# newx 
#    1 

coefficients(out)[["newx"]]
# [1] 1

More generally, use unname():

unname(coefficients(out)[c("newx", "(Intercept)")])
# [1] 1.0 1.5

head(unname(mtcars))
#                     NA NA  NA  NA   NA    NA    NA NA NA NA NA
# Mazda RX4         21.0  6 160 110 3.90 2.620 16.46  0  1  4  4
# Mazda RX4 Wag     21.0  6 160 110 3.90 2.875 17.02  0  1  4  4
# Datsun 710        22.8  4 108  93 3.85 2.320 18.61  1  1  4  1
# Hornet 4 Drive    21.4  6 258 110 3.08 3.215 19.44  1  0  3  1
# Hornet Sportabout 18.7  8 360 175 3.15 3.440 17.02  0  0  3  2
# Valiant           18.1  6 225 105 2.76 3.460 20.22  1  0  3  1

## etc.

An easy and rather direct way to do it is

as.numeric(out$coefficients["newx"])

If the question is about removing names, another way is here

my_vec <- # some quantile function(returns named vector)
names(my_vec) <- NULL
my_vec
## [1] 1 2 3