name for histogram of nominal p-values under the null To evaluate a statistical test or means of generating frequentist confidence intervals, it makes sense to repeatedly simulate data for which the null is true and then compute the nominal p-value, and generate a histogram of these p-values. For a valid test, this distribution is basically flat (uniform). There is good discussion of this point here. Within either the frequentist or Bayesian literature, is there a name for this type of histogram/ method for assessing nominal p-values? A citation for when this approach was first proposed/ implemented? 
 A: This idea of the uniform distribution for P-values is fairly new
in statistics education and practice. I don't know if anyone has yet made up a name
for the related histograms that has come into general use. Below I just call them "Null P-value" histograms.
It is important to note that this uniform distribution for P-values holds only if
the null hypothesis is true, the test statistic is continuous, and all of the assumptions for the test are met.
Ordinarily, the test statistic must be exact and continuous, as in a one-sample t test or ANOVA.
Tests involving discrete distributions and certain approximations have useful P-values for hypothesis testing, but often the P-values are not uniformly distributed across the interval $(0,1).$ 
Below are a few examples.  All
tests shown are standard tests in R, with P-values 'extracted' using $ notation.
Code for the histogram is shown only in the first example; except for the header the code is the same in all examples. 
Shapiro-Wilk test for normality: $H_0$ true because data are normal. Too many P-values near 1.
set.seed(1212)
pv = replicate(10^5,  shapiro.test(rnorm(20))$p.val)
mean(pv < .05)
[1] 0.04924
hist(pv, prob=T, col="skyblue2", main="Shapiro-Wilk Null P-values")
  curve(dunif(x), add=T, col="red", n=10001)


One-sample Wilcoxon test: $H_0$ is true because population sampled has median 0. Discrete rank-based test statistic.
set.seed(1212)
pv = replicate(10^5,  wilcox.test(rnorm(20), mu=0)$p.val)
mean(pv < .05)
[1] 0.04905


Binomial test: Discrete test statistic, $H_0$ true because $p = 1/2.$ Because of discreteness a test at exactly the 5% level is not available.
set.seed(1213)
pv = replicate(10^5,  
   binom.test(rbinom(1,20,.5), 20, p=.5, alt="two")$p.val)
mean(pv < .05)
[1] 0.04169


Pooled 2-sample t test: Assumptions not met because variances unequal. $H_0$ true because means equal. This test rejects more often than 5% of the time. (Note: In R, the default two-sample t.test is the Welch test; the parameter var.eq=T invokes a pooled test.)
set.seed(1213)
pv = replicate(10^5, 
     t.test(rnorm(20,100,2), rnorm(10,100,20), var.eq=T)$p.val)
mean(pv < .05)
[1] 0.18476


Welch 2-sample t test: P-value has uniform distribution on $(0,1).$ Continuous test statistic. Assumptions met. $H_0$ true. Technically an approximate test,
but very nearly exact.
set.seed(1214)
pv = replicate(10^5, t.test(rnorm(20,100,2), 
     rnorm(10,100,20))$p.val)   
mean(pv < .05)
[1] 0.04939


Reference: Murcoch DJ, Tsai Y-L, Adcock J:
P-values are random variables (2008), The American Statistician, 242-245, has several histograms similar to those shown here. This paper contains an early emphasis, if not the first, on regarding P-values as random variables, using Monte Carlo
simulation to obtain their distributions in various cases, and the standard uniform distribution of P-values from continuous test statistics under the null hypothesis. The caption of Figure 2 in that paper refers to "Histograms of p-values under the null hypothesis." 
An earlier paper in the same journal, 
Sackrowitz H & Samuel-Cahn E (1999), P-values as random variables---Expected P-values, 326-333, 
does not contain such histograms. 
A: 
...is there a name for this type of histogram/method for assessing nominal p-values?

The true distribution of a quantity under a (simple) null hypothesis is called the null distribution of that quantity.  There is no specific name for the histogram of a Monte-Carlo simulation of the distribution of the p-value.  It would usually be named by description: the histogram of a Monte Carlo simulation of the null distribution of the p-value.
