The judge, Mr Justice Laddie, made his comments as the Daily Mail publisher tries to stop Desmond using the "Mail" name in the title for his new London evening newspaper, which will challenge Associated's Metro and the Evening Standard.
Mr Justice Laddie was told by Anthony Watson QC, counsel for Express Newspapers, that there was no record of any intention to call it The Evening Mail.
Despite there being no record, Express Newspapers appointed Nick Ferrari, the former Sun journalist and LBC 97.3FM talk radio host, as editor of the planned launch in early February.
Brand Republic reported from sources in November that Express Newspapers plans to call its new title, which has been talked about for months, the Evening Mail or London Evening Mail.
Associated's lawyers are arguing that Express Newspapers is trying to "pass itself off" and confuse readers and advertisers into thinking it is related to the Daily Mail. It is seeking an injunction to stop Express Newspapers using the name.
On the second day of the hearing, Mr Justice Laddie told Mr Watson: "I find it difficult to understand how your clients could have got within a month of launching what must have been an important newspaper and had got so far as appointing an editor and yet your clients say that there's not a single internal document in which the choice of name was even mentioned."
Desmond has denied that a name has been decided on for the new title and is arguing that Associated has no trademark rights over the name "The Mail".
On Tuesday in court, Desmond's lawyers pointed to the other examples of newspapers using the "Mail" name up and down the country, including long-established titles such as the Birmingham Evening Mail and Scottish title the Sunday Mail, both of which are owned by Trinity Mirror.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the .