Trying to display a name in a calendar if several criteria are met (edited)

Hello all, I've learned alot from this forum over the last year but I have one that I can't seem to jiggle into working and wanted to see if I can get some insight. I'm making a sharepoint facing Time-Off calendar and am almost done but I'm at the point where I'm trying to figure out how to structure displaying the names that get approved off, under the dates they were approved for. Part of me feels like it has something to do with the way we count between days vs how many days.

For example, if you have the 1st through the 10th off, you could =DAYS this, however, the very first day is not counted. It would result in 9, when in fact, you have 10 days off, 1-10. So when I tell a calendar date formula to display the following formula:

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The 'greater than or equal to' or 'less than or equal to' isn't registering correctly. I THINK, that's just a hypothesis.

If anyone can take a look and give me some direction, that would be fantastic. In my attached sheet, two examples are actually showing correctly for their respective dates, and I can't figure out why those happen to show correctly, while the others do not.

For a the latest Sup name based on your criteria: =IFERROR(LOOKUP(2,1/(P9>$V$14:$V$136)/(P9<$W$14:$W$136)/($Y$14:$Y$136="APPROVED")/($Z$14:$Z$136="O"),$S$14:$S$136),"")

For multiple results for same data, an array formula entered with Ctrl+Shift+Enter. But this will may slow your file. Wrap it in a iferror formula as well:
=IFERROR(LOOKUP(2,1/(Q9>$V$14:$V$136)/(Q9<$W$14:$W$136)/($Y$14:$Y$136="APPROVED")/($Z$14:$Z$136="O"),$S$14:$S$136),"")