Why cant I register xyz.com?
The most popular top-level domains have already been heavily exhausted. It is very difficult to find any generic words that are still available to register. Additionally, most short words/phrases have also been secured. For example, if you sell widgets, you can gaurantee that www.widgets.com has already been taken.
How many companies trade under the same name, or abbreviation?
Competition is tight and you should not set your heart on a singular name. Take your time and come up with a number of alternatives or variations.
For example, if you company name was “joe-bloggs” and that domain was not available you could go for “joe-bloggs-catering” if that was your trade.