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.