Can I run an Uzbek company in English?

Nothing stops a foreign owner deciding, corresponding and keeping management records in English — and the founding documents are commonly drafted bilingually so the owner reads what they sign. What the registration act requires is that the version reaching the registrar is in the state language, on the first filing and on every later one; the register then holds a foreign-language company name too where the founding documents give one. The rest of the state’s side does not switch: statutory filings go to the tax authority in the official language, the taxpayer cabinet runs in Uzbek and Russian, and the books behind the returns follow Uzbek accounting standards. (Registration Regulation, Paras. 12, 21 — lex.uz ↗)

The practical division of labour follows from that: English is workable as the language of ownership and decisions, while whoever prepares the filings reads the law and the cabinet in the original. Documents crossing the border — powers of attorney, registry extracts — are translated into Russian or Uzbek on the way in.