Organisations wishing to buy web addresses ending in their brand names have until the end of Thursday to submit applications.
For example, drinks giant Pepsi can apply for .pepsi, .gatorade or .tropicana as an alternative to existing suffixes such as .org or .com.
Parties are able to request up to 50 web address endings.
The Internet Corporation for Assigned Names and Numbers plans to publish application details on 30 April.
Companies had to sign up to its process by March to qualify for the upcoming deadline. It says 839 users are taking part.
Canon and Google are among the companies to have said that they paid the $185,000 (£116,355) fees required to take part in the process.
Nominet, the organisation which manages .uk domains, confirmed it was applying for .wales and .cymru .
ICM Registry - the firm which already oversees .xxx addresses - announced it had also applied for .sex, .porn and .adult. It said it wanted to offer them "free of charge" to its existing customers.
Successful applicants face $25,000 in costs per year to maintain the generic top-level domains.
"We plan to apply for Google's trademarked gTLDs, and we're currently exploring opportunities to apply for new ones as well," the search giant told the BBC.
"We want to help make this a smooth experience for web users - one that promotes innovation and competition on the internet."
Other organisations were less forthcoming - Facebook, the BBC and Coca-Cola would not comment on their plans.
"We do not disclose details of any proprietary marketing plans until they are public facing," the drinks maker said.
The process has the potential to cause problems among firms that share brand names. The US and German firms that both operate under the name Merck have already clashed over ownership of a Facebook page.
The German firm confirmed it had applied for .merck and .emerck.
The US company's spokesman, Ron Rogers, told the BBC: "We're monitoring the Icann gTLD application process with interest."
Anheuser-Busch InBev and Budejovicky Budvar may face similar conflict over their claims to own the Budweiser beer brand.
Icann suggested that in such cases the firms involved should try to negotiate a deal by themselves. If they fail, it said it would hold an auction for the suffix as a "last resort".
"We don't want to be judge and jury - we want the applicants to work it out on their own," an Icann spokesman told the BBC.
Efforts to launch the new naming system have been mired in controversy.
In November, 87 business associations and companies sent a petition to the US Department of Commerce complaining that the program entailed "excessive cost and harm to brand owners" .
Signatories included the tech giants Adobe, Hewlett-Packard, Dell and Samsung.
The department subsequently snubbed Icann by cancelling a bidding process that was expected to extend the organisation's right to run the Internet Assigned Numbers Authority - the contract which allows it to manage the domain name system.
Although Icann retains control for now, its mandate runs out in September.
However, the organisation rejects claims that its move to introduce new suffixes was badly thought out.
"This programme is the result of six years of careful study and deliberation which involved more than 2,400 public comments and dozens of public comment periods," a spokesman told the BBC.
"It was neither hasty nor ill conceived."