Okay, so I'm going to assume that you're using some version of MS-IME. Essentially, it doesn't matter what setting you have the input method set on - hiragana or katakana. Both can be turned into the other. The first thing you have to make sure is that you have it set to romaji input, and not kana input. (Check the Properties.) Romaji input allows you to type in romaji and have it turn into kana. Typing k and o gives you こ, for example. Kana input is when each kana is mapped to different key, and takes some getting used to.
When you have it set to romaji input, and have the IME set to type Japanese script, the space bar is used to turn kana into kanji (or the other type of kana). For example, if I want to type Tokyo in Japanese, I would type to, u, kyo, u, and it would come out as とうきょう with a red line underneath. This red line indicates that the kana can be changed to kanji or katakana. By hitting the space bar, とうきょう becomes 東京, and then I hit "Enter" to confirm.
For example, if I want to write "Josh" in katakana, I simply type "jo" and "shu", and it comes up じょしゅ. Then I hit the space bar, and among other kanji options there is also the katakana version of ジョシュ, which I can select and confirm by pressing enter.
Whether the input is set to hiragana or katakana simply changes what the default kana are. They can still be changed to kanji, or the other kana. If I set it to katakana, then when I type to, u, kyo, u, it comes out トウキョウ, but when I hit the space bar it becomes 東京.
So, when you have it set to romaji input, and whichever kana setting you want (hiragana or katakana, either will work), then you just have to type out your name in romaji to get it to come up right, and don't hit the space bar unless you want to change the characters to something else.
With standard English transliteration conventions, "Connor" would be transliterated into Japanese as "Konaa", that is, ko, na, and then a lengthing bar at the end. (You get this in the IME by hitting the hyphen key). It would look like this コナー.
I don't know exactly how "Haberland" would be pronounced. If it's like "HAY-ber-land", then it would be "Hebaarando" ヘバーランド, possibly even Heebaarando ヘーバーランド, with lengthening bar after the "e". If it's like, "HAH-ber-land", then it would be Habaarando, ハバーランド.
"Ru" is used to transliterate initial "ru", initial "lu", and final "l". If I saw konaru in katakana, I'd expect some name like "Conal".
Hope this helps.