Counting number of columns a value appears in (Google Sheets) - google-sheets

Question

I have a Google Sheet where I want to know the number of unique columns that a value appears in. For example, given the following sheet:
| A | B | C | D |
+-------+-------+-------+-------+
| Joe | Lisa | Lisa | Lisa |
| Joe | Lisa | Jenny | Lisa |
| Joe | Jenny | Jenny | John |
| Joe | Jenny | Katie | John |
| Joe | Jenny | Katie | John |
I would want something that counts Joe appearing in 1 column, Lisa appearing in 3, Jenny appearing in 2, Katie appearing in 1, and John appearing in one, i.e.
| Name | Count |
+-------+-------+
| Joe | 1 |
| Lisa | 3 |
| Jenny | 2 |
| Katie | 1 |
| John | 1 |
What's the best way to do this?

Answer 1

Assuming the data has no spaces in it, try:
=ArrayFormula(QUERY(SPLIT(UNIQUE(TRANSPOSE(SPLIT(JOIN(" ", QUERY(A1:D&"_"&COLUMN(A1:D1),,ROWS(A1:A)))," "))), "_"), "Select Col1, count(Col2) where Col2 > 0 group by Col1 label count(Col2)''"))
If the source data has spaces, try:
=ArrayFormula(SUBSTITUTE(QUERY(SPLIT(UNIQUE(TRANSPOSE(SPLIT(JOIN(" ", QUERY(SUBSTITUTE(A1:D, " ", "~")&"_"&COLUMN(A1:D1),,ROWS(A1:A)))," "))), "_"), "Select Col1, count(Col2) where Col2 > 0 group by Col1 label count(Col2)''"), "~", " "))

Answer 2

EDIT
As Tom has noticed, I've missed the task, and the correct formula is:
=QUERY(
QUERY(
{TRANSPOSE(SPLIT(TEXTJOIN("#",1,FILTER(COLUMN(A:D)*row(A:D)^0,A:A<>"")),"#")),
TRANSPOSE(SPLIT(TEXTJOIN("#",1,A:D),"#"))},
"select Col1, Col2, count(Col2) group by Col1, Col2"),
"select Col2, count(Col3) group by Col2 label Col2 'Name',count(Col3) 'Count'")
Credit: #tom-sharpe
My original formula counted max times name is in a row:
=QUERY(
QUERY(
{TRANSPOSE(SPLIT(TEXTJOIN("#",1,FILTER(COLUMN(A:D)^0*row(A:D),A:A<>"")),"#")),
TRANSPOSE(SPLIT(TEXTJOIN("#",1,A:D),"#"))},
"select Col1, Col2, count(Col2) group by Col1, Col2"),
"select Col2, max(Col3) group by Col2 label Col2 'Name'")