That's not an easy answer for many bloggers, and some don't accept it without a lot of arguing. The other side of the coin is that any available URL is there for the taking, by anybody. Relevance of the name in question, to any physical existence outside the Internet world, has no validity.
Today, we have a query of an issue not previously argued.
I have website "TheNameThatIHave.com". Today, I discovered that somebody else is publishing to "TheNameThatIHave.blogspot.com". That's not right - I should have the right to "TheNameThatIHave.blogspot.com"!
And the answer here is
No, if somebody else has "TheNameThatIHave.blogspot.com", it's their URL. You have no claim to "TheNameThatIHave.blogspot.com", simply by having "TheNameThatIHave.com".
Every top level domain has its own subdomain directory.
There are multiple top level domains on the Internet, as well as various country based top level domains, and numerous web hosts similar to Blogger. Each domain / host has their own name directory, and assigns / allows assignment of names from its own universe.
Assignment of any name in one top level domain / sub domain directory is irrelevant to eligibility to the same, or similar, name in any other directory. There is no screening, to determine the validity of anybody to publish to "TheNameThatIHave.blogspot.com", for any value of "TheNameThatIHave".
If the BlogSpot subdomain of your choice is available, you may have it.
If the URL "TheNameThatIHave.blogspot.com" is available for publishing, every blogger has equal claim to take it. If you see it, and you take it, you have it - for eternity. The moment you take it, nobody else has any claim over it - for eternity.
If somebody else took it, you have no claim over it - even if you own "TheNameThatIHave.com".
As the well used adages go
First come, first served.
You snooze, you lose.