Why is h2o hydrogen Dioxide instead of di hydrogen oxide?

It isn't.

Hydrogen dioxide (or more accurately dihydrogen dioxide) is H2O2, more commonly called hydrogen peroxide.

H2O could be accurately called dihydrogen oxide or dihydrogen monoxide.

H2O is Dihydrogen monooxide (AKA Dihydrogen oxide). The "Di" means there are 2 atoms of hydrogen. If you want to be picky, you can put "mono" in front of "oxide". "Mono" means one.

And the reason 'oxide' ends with 'ide' is because that's what you always do to the element name if there are only 2 elements in a compound.

H2O2 is Hydrogen peroxide. The "per" means there is one oxygen atom for each hydrogen atom.

Hydrogen Dioxide would be HO2. However, this simply cannot exist because the only hydrogen atom can lose one electron, but you have 2 oxygen atoms, each needing 2 electrons. You'd simply be cut short.

And a rule of thumb: Capitalize the first letter of the first element name in a formula, but the rest is lowercase.