More of a general word.
Outer space will have Kanji and rental space may too.
However, you can use it in your English name:
オゥータースペース, which if I correctly typed it is literally "Outer Space" in English, without referring to being in space. A brandable name in Japan have you.
It's difficult for me to say with 100% certainty that this is just how you pronounce it as Katakana is/was mainly used for that.
With more English words sounding better, Japanese is evolving. Instead of keitai for cellphone, most refer to it as a sumatofuon.
(Hard to type on a Japanese cellphone keyboard)