The formulas SGIII and I posted the first time and the Excel formula I found on the Internet all will find the most commonly occurring name in a table if all those names are a single column. None work for an array of names. I'd like to see the Excel formula you are referring to that works on an array of names. It might lead to a better/different answer here.
SGIII has now posted an easy way to do it if you have a separate list of all the names. Below is a method that does not require the names to be placed in a list. It is more complicated, though, and has the limitation of 999 columns and 999 rows. I did not design it for your exact table, it is only an example. And there may be a better way to do it; there often is.

Table 2::B2 =COUNTIF(Table 1::$B$1:$E5,Table 1::B2)+ROW()÷1000+COLUMN()÷1000000
drag-fill to the other data cells in the table.
This counts the occurrences of that particular name and appends the row number/1000 and column number/1000000 so that every number in the table will be unique. The largest number in the table indicates the location of the name occurring most frequently.
Table 2::B1 =MAX(B)=MAX($B:$E)
fill to to the right to complete the row
Table 2::A2 =MAX(2:2)=MAX($B:$E)
fill down to complete the column
Table 2::A1 (the answer) =OFFSET(Table 1::A$1,MATCH(TRUE,A2:A5,0),MATCH(TRUE,B1:E1,0))
This will work okay as long as the size of the array of names in Table 1 stays the same. If you change it, you also have to modify Table 1 and the formulas in it so it matches up. You can put Table 2 out of the way on another sheet and reference cell A1.