In chapter 301 we finally learn some more about Rei's background, or more importantly (for this little piece of meta): her maiden name.
And since I was reading the English translation, that's all the info on the name that I got within the manga/text.
In that context, the name appeared highly ironic. The Kanji spellings for Himura that immediately come to mind (and as far as I tell are commonly used) are 日村 and 火村.
日村 when taken apart is sun/day + village, 火村 is fire + village. Given BnHA naming conventions, it's a name more befitting someone with Endeavor's background/quirk.
But no, it's not actually spelled with these Kanji. The ones Horikoshi actually uses here are 氷叢, meaning ice + crowd/gathering.
So, while the Kanji do indeed fit Rei's ice, the way it's read is like a reverse-foreshadowing of Endeavor's fire. Very Horikoshi, very BnHA.