I know everyone hates Wikipedia for validity, but here's a snippet from the wikipage:
'housecarls (Old Norse: húskarlar, singular húskarl; also anglicised as huscarl (Old English form) and sometimes spelled huscarle or houscarl)'
So, multiple spellings, of course. But for a Norse clan, the most common would be to refer to a húskarl or the group of húskarlar.