How important is a trademark on the company name for a startup?

TMs are important because they identify your company, they identify your brand. While TMs can be expensive, you may be able to initially get by with a TM registration in a single country just as a means to get your company name or brand out in the world, however, TMs, like patents, are territorial - you only actually have substantive rights within the country where the TM is used and or registered. Registration also provides notice to the world that the particular TM is yours - if you do not register the mark, the world will not necessarily "know" that you exist, and while TMs "attach" or begin to provide protection based upon usage, it may be more difficult to prove your existence, and your rights to the TM, without a registration.

As a startup, you will put money and effort building your own brand from scratch and you don't want anyone to misuse your name later on. But also for the sake of cost, i would recommend registering the trademark in your home country and to also go for the U.S. where many companies host their websites and most of the giant cloud service providers are. This will at least guarantee that if someone misused your brand and their websites are hosted at one of those countries then you will be able to take an action against them. Later on, if your business model and strategy is to license your services in other locations then you might be looking at other countries to register your trademark.

It completely depends on the products or services and the countries of interest. Some countries recognize rights through use. Other countries are first to file to establish rights. Some B2B products or services are less likely to be the target or pirates or infringement actions. Still, in most cases, you have 6-months from filing to internationally file so try working that into your timeline and budget.

Although it is highly recommended to start commercializing products or services with a registered trademark it is indeed expensive. When short of money, you may begin to operate without a registered trademark but once you have the funds you should apply for your brand's registration as soon as possible since this a very important and delicate matter.