Answer
$18,278$
Work Step by Step
The number of arrangements of $n$ objects in $r$ slots where each slot can be any one of these objects is $n^{r}$.
Number of company names represented by 1 letter
$26^{1}=26$
Number of company names represented by 1 letter
$26^{2}=676$
Number of company names represented by 1 letter
$26^{3}=17,576$
Total: $26 + 676 + 17,576 = 18,278$