It's also in other versions like RV, ASV, NASB in italics and bracketed, denoting that it's an addition by translators.
Authorised KJV also has italics words for such words. The Greek "kai" for and is sometimes translated as even, but it's not in this verse. It is solely for the English style purpose to emphasize or rather simply as epexegetical (explanatory) word like "that". However, such overly literal translation that corresponds to the Greek phrase structure caused such rendering; it is unnecessary and outdated. Greek sentence structure is very flexible and different from English. I would encourage KJV readers to switch to the better ESV. Notice, how the ESV simplifies the sentence in a flow:
ESV: But to all who did receive him, who believed in his name, he gave the right to become children of God.
NASB: But as many as received Him, to them He gave the right to become children of God, [even] to those who believe in His name
Cambridge Dictionary defines Even:
even adverb (MORE EXACTLY)
used when you want to be more exact or detailed about something you have just said:
I find some of his habits somewhat unpleasant, disgusting even.
She has always been very kind to me, even generous on occasion.
even as
at the same time as:
I tried to reason with him, but even as I started to explain what had happened he stood up to leave.