Im registering a dot com company name for a company in Costa Rica? Can i be sued ..

[River]

US company.exists,same nam A friend told me he registered a dot com for his company in argentina and just used a dot com. There was an identical named company in the US and he said they shut down his site. Are there laws againt this, i have no intention to claim to be or defraud the US company. EX: ALLIANCE GROUP exists in US but dont own the dot com, can i buy the dot com to advertise my company with the same name..again im not claiming to be them.
I was told i need to address it as alliancegroup.ar.com and not alliancegroup.com even though its available. Im only using an example name here. LEGAL ANSWERS ONLY PLEASE