It would sound pretty odd, at least. "Er født" would refer to children that are already outside ("Hun er født i januar"), but in this sentence you want to talk about children that are in the act of being born. Or differently expressed, "at være født" is a state while "at blive født" is a process.
For a hint, you can try to insert 'being' into the sentence, and if it still means the same, you should use blive.
Men flere af dem bliver opkaldt Arya eller Sansa. http://www.dr.dk/Nyheder/Ligetil/Dagens_fokus/Kultur/2015/08/Flere_nyfoedte_faar_navne_fra_tv_serie.htm
They end with -t here because they're past participles now. At blive is the conjugated verb here. This variant functions likes in English: "Children are (being) born" - "Børn bliver født".
In the other, blive-less variant, the full verb is the conjugated verb, so it gets its proper passive (or reflexive) ending: "Døren åbnes" - "The door opens/is being opened."
There is not a lot of difference between the two, but there are ways to make it clearer what's happening.
First off, a bit of explanation: the -es conjugation you learnt for the passive is historically (and probably more accurately) a reflexive suffix. "Døren åbnes" is derived from an earlier form of "Døren åbner sig" - "The door opens (itself)."
The bliver-form is more of a true passive. At blive is literally "to be/to become". So if you say "Døren bliver åbnet", you imply that there's someone who actively opens the door. You can get this meaning by going for active grammar, too, "Nogen åbner døren", but that's pretty un-Danish. Well, unless you care about that person. :)