Well, who pays tax is kind-of a complicated question. VAT is collected at many points along the supply chain (and sales tax typically at just one). But who pays economically depends on a bunch of elasticities: if the consumers will buy X at any price, then the tax lands on them, whereas if they will only pay at maximum Y (otherwise they go without) then the tax lands on the seller. (But in reality, nothing is at either endpoint.)

It's called "value added" because it's a tax on profit, and everyone in the supply chain pays it.

The companies in the middle of the supply chain can reclaim any VAT they paid on goods/services used in the business [1], so effectively they don't pay it.

VAT is definitely not a tax on profit, that's usually called "corporate tax" [2] which is a completely different thing.

[1] https://www.gov.uk/reclaim-vat

[2] https://en.wikipedia.org/wiki/Corporate_tax

Revenue tax is charged in the same location as VAT though, you just cannot offset it with the VAT you pay (or between two companies, it’s never zero).