This exists in 5e, but does not have a specific name
The 5e DMG has the following passage, under "Multiple Ability Checks" (page 237 - emphasis mine):
Sometimes a character fails an ability check and wants to try again. In some cases, a character is free to do so; the only real cost is the time it takes. With enough attempts and enough time, a character should eventually succeed at the task. To speed things up, assume that a character spending ten times the normal amount of time needed to complete a task automatically succeeds at that task. However, no amount of repeating the check allows a character to turn an impossible task into a successful one.
Thus, if a character has any chance of succeeding at a check, the DM estimates how long one check would take, multiplies that by ten, and declares the character to be successful after that amount of time.
Since "any chance of success" implies that a character would succeed on a roll of 20N, this is essentially the "Take 20" mechanic from 3e/3.5e as described in KRyan's answer, but taking ten times as long as a regular check rather than twenty.
The 3.5e rules on "taking 10" and "taking 20" explicitly say that Take 10 and Take 20 cannot be done when a character is "threatened or distracted". The 5e DMG rule does not make this explicit, but it is implied in "the only real cost is the time it takes" (i.e., there is no cost of prolonged exposure to threat and distraction).
However, there are two important differences between the editions. First, while the 3e/3.5e rules explicitly say that you can "calculate your result as if you had rolled a 20", the 5e rules merely say that the character "succeeds", without making reference to a specific roll. The standard in 5e is for a successful skill check to simply be "successful", with no special consequence or outcome for a 20N. If there is an 'even better' success possible with a 20N (and see Does the degree of success or failure on a skill check matter?), however, then that would be triggered by a 3e/3.5e Taking 20, but not by the 5e procedure, since the 5e method doesn't assume a specific roll.
Second, the 3.5 rules assume that the character will fail before succeeding, and thus must apply any results of failure before the "Take 20" success is achieved. In 5e, in contrast, the unnamed equivalent may only be done, as previously mentioned, if there is no real cost to failure other than more time.