No one knows for sure because a denomination could be formed by 2 families meeting in someone's living room who believe the same thing, but differ slightly from the local churches in that area.
Therefore there is no requirement for a church to "register" itself centrally. In fact in SOME countries.. registering or announcing you are a church might carry social sanctions or cause the government to scrutinize you more closely.. so in those countries..staying below the radar is a good thing.
In the US, the IRS has over 30,000 registered denominations..but that's probably not all of them.
So at least 30,000 in the US alone.
Here is a quick list of the Biggees off the top of my head...
Catholic (I'm lumping RCC, Eastern rite, Chinese, Russian Orthodox Catholic denominations into 1 grouping )
Those are the biggees..but there are many other groups.
Protestant or Protestantism is a word that Catholics use to denote ANY non-catholic christian which broke away some time after the protestant reformation of the 1500s. Protestantism is not just 1 denomination but a category of denominations.
Worldwide, The Catholic denominations account for roughly 2/3rds of Christianity all by themselves. I think there are 1billion Roman Catholics alone, worldwide.