One name for this case is alternating case. A text converter that uses the form (Alternating Case Converter) explains:
The alternating case converter converts text, so as a result the initial letter is a capital one and from there on the cases alternate between uppercase and lowercase. For this, a text needs to be entered into the form. Alternating case writing is particularly common on the Internet and is used by those who think it looks "cool". It is also known as Alternating Caps and Troutspeak.
Other converters (like this and this) also call it alternating case.
This usage is also attested in published work on typography and reading. Mary C. Dyson and Ching Yee Suen in Digital Fonts and Reading (2016) describe a study that assessed reader eye movement when reading alternating case.
McConkie and Zola  presented passages of text in aLtErNaTiNg CaSe then on specific saccades the case alternation was switched (AlTeRnAtInG cAsE). The astonishing finding was that fixations following a case switch were no longer than fixations that did not follow a switch. [...] However, as you might guess, reading alternating case is more effortful than reading all lower case or all uppercase text [Rayner, McConkie, and Zola, 1980; Juhasz, Liversedge, White, and Rayner, 2006; Reingold, Yang, and Rayner, 2010]. It may be that alternating case disrupts normal word identification processes [Coltheart and Freeman, 1974] [... ]
These sources cited by Dyson and Suen show that scholarship in the mid-1970s was already using the term "alternating case." Here is the first study mentioned from 1979, McConkie, George W., and David Zola. "Is visual information integrated across successive fixations in reading?." Perception & psychophysics 25.3 (1979): 221-224, from the abstract:
College students read a passage presented in AlTeRnAtInG cAsE on a CRT while their eye movements were monitored. During certain saccades, the case of every letter was changed (a became A, B became b). This change was not perceived and had no effect on eye movements. Apparently visual features of the type which specify the difference between upper- and lowercase letters are not integrated across fixations during reading.
And here is the earliest study mentioned, Coltheart, Max, and Roger Freeman. "Case alternation impairs word identification." Bulletin of the Psychonomic Society 3.2 (1974): 102-104:
The prose passage was on the left page of a booklet, in upper case, lower case, or alternating case.
This experiment, then, has shown that the alternating-case condition does, in fact, lead to impaired word identification, even when character size is the same for upper- and lowercase characters.
So alternating case specifically describes the case of switching case with each letter, whereas words like studly case more generally describe the introduction of case internal to words or without spaces through a predictable pattern.