To become an officially recognized business entity, you must register with the government. Corporations will need an "articles of incorporation" document, which includes your business name, business purpose, corporate structure, stock details and other information about your company. Otherwise, you will just need to register your business name, which can be your legal name, a fictitious "doing business as" name (if you are the sole proprietor), or the name you've come up with for your company. You may also want to take steps to trademark your business name for extra legal protection.
obrt: ≈ sole proprietorship; several types: slobodni, vezani, and povlašteni obrt (free, tied, and privileged proprietorship registered according to profession; tied and privileged proprietorships are those only master craftsmen can register,) paušalni obrt, obrt-dohodaš, obrt-dobitaš (flat-rate proprietorship, income tax p., profits tax p.; these are registered according to the type of taxation; first two are obligated to pay income tax and the last one is obligated to pay profits tax), sezonski obrt (seasonal proprietorship, that runs for a limited number of months during a year)