As mentioned in the article, an executive editor of the Associated Press itself argues that the move is a First Amendment violation. As I wrote in a different comment:

Whenever holding press conferences in the Oval Office, the government creates a nonpublic forum [1] and invokes freedom of the press (because a news organization who is allowed to attend should be able to share what happened). The government can deny a news organization entry based on the subject of the speech (e.g. no reporting about the Gulf of Mexico/America, regardless of the name used) but cannot deny entry based on the news organization's viewpoint (e.g. thinking that Gulf of Mexico is the more appropriate name allowed, thinking that Gulf of America is the more appropriate name not allowed).

I can't reply to GP directly, but I'd like to directly address an assertion that GP made:

> The AP has no right to the Oval Office. They are not an elected entity nor have any legal standing.

The AP has no right to the Oval Office in the absolute sense, but if the government allows some news organizations (at least 1) into the Oval Office for press conferences then the criteria for allowing news organizations must not discriminate based on viewpoint. So long as AP meets the criteria that obey the First Amendment, then AP is entitled to enter the Oval Office for press conferences.

[1] https://en.wikipedia.org/wiki/Forum_(legal)#Nonpublic_forums

From the AP article:

> “It is alarming that the Trump administration would punish AP for its independent journalism,” Pace said in a statement. “Limiting our access to the Oval Office based on the content of AP’s speech not only severely impedes the public’s access to independent news, it plainly violates the First Amendment.”

It certainly has a chilling effect, if the president can apply arbitrary limitations on news agencies just because they refuse to comply with specific naming orders.