There were lots of rumors about the number 290, most being some variation of the claim that it was a secret cabal of 290 British merchants who had pooled their money to build Alabama. (It's mentioned in this version of "Roll Alabama, Roll," though the number is given as 292.) Keep in mind that, although her construction as a Confederate warship was a fairly open secret in the UK, she was not formally named Alabama until she was put in commission in the Azores, after leaving Britain. So until her official name became widely known, she was commonly referred to as 290.
The actual reason is prosaic -- 290 was her designation in the shipyard, being the 290th keel laid by John Laird, Son & Co. at Birkenhead.