Not quite — Kuwait Companies Law No. 1 of 2016 places clear restrictions on company names. Under Article 12, your company may not use the same name as, or a name confusingly similar to, another company if that company operates in the same business activity. The only exception is if the other company is already in liquidation and has given written approval for the name use.
If you do choose a new name or later decide to rebrand, Article 13 allows a company to change its name by following the same procedures used to amend the Company Contract. Importantly, a name change must be officially proclaimed (publicly announced), and it does not affect any existing rights, obligations, or legal proceedings the company was already involved in.
For expats, the practical advice is to conduct a name availability search through Kuwait's Ministry of Commerce and Industry before investing time in incorporation paperwork. Choosing a name that is too similar to an existing competitor in your sector will result in rejection. Also note that the law requires announcements to be made in two local daily Arabic newspapers (Article 1), so budget for proclamation costs as part of your setup process.
This is general legal information, not legal advice. For advice on your specific situation, consult a lawyer licensed in Kuwait.