Looking on the internet deeply has found these results:

it's given the name is the most popular phrase on the web.

it's given a name 1227,000 results on the web	it's given the name 1441,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
I've been given a name. He had given a name to each of the Brothers. It's more of a given name. You have not given a name for the info text file, please set one. Because it's been given a name doesn't mean it's not a Borg. You have not given a name for the cover, please set one. This medium was given a name the ether.	Their commander and the best fighter is given the name QINGLONG They were given the name by the press after a heist where they all wore ridiculous pompadour wigs. It's the name given by His Majesty to the collective parties opposed to the peace between the North and South. 'My father was given the name Prince.' Joe: How are you given the names? He was given the names of 14 scientists. How are you given the names? He was given the names of 14 scientists.

it's given a name

1227,000 results on the web

it's given the name

1441,000 results on the web

More popular!

Their commander and the best fighter is given the name QINGLONG
They were given the name by the press after a heist where they all wore ridiculous pompadour wigs.
It's the name given by His Majesty to the collective parties opposed to the peace between the North and South.
'My father was given the name Prince.'
Joe: How are you given the names?
He was given the names of 14 scientists.
How are you given the names?
He was given the names of 14 scientists.