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 [1979] 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.

See also the below for non-strictly-alternating capitalization:

• "Erratically capitalized", as in NY Mag:

  (The idea, so far as there is one, is that the erratically capitalized line is meant to represent a sort of mocking imitation of the original line.) This is now the canonical format of the Mocking Sponge meme.

• "Randomcase", as in Unit Conversion:

  With random case the rules of grammar that determine upper and lower case do not apply. Upper case or capital letters appear in a random sequence. Lower case letters also appear in a random sequence. Random refers to a pattern or series that has no pattern. This can be helpful for creating security codes. The random qualities can be unique. Randomness traditionally was generated through devices such as dice but computed randomness today can easily create randomness for statistical sampling, simulations, and cryptography.

When used in the context of memes, you can refer to it as Spongebob case.

See for example:

• SpongeBob case — Jo Lokito's blog

• SpongeBob case — GitHub

• Rdrr.io — SpongeBob

Another name is Ransom Note font; from the trope of ransom notes made by cutting and gluing random words and letters from newspapers, to foil attempts at analyzing the kidnapper's handwriting.

As decapitated_soul points out,

It's also called Anarchy case.

Other names for studly caps:

1. StUdLyCaPs

2. Sticky caps

3. Anarchy case

4. Altcaps

5. Alternating caps

DB Pedia

It is also called arbitrary capitalization.

From Tech Republic:

1: Even if you're wrong, be consistently wrong Unless your goal is to produce a whimsical ransom note effect (and what boss doesn't love that in a report or memo), arbitrary capitalization is distracting and annoying. And stupid looking. If you're not sure whether it should be Enterprise Resource Planning or enterprise resource planning, at least pick one and stick with it. (Note: There's really no good reason to capitalize that term unless it's part of a title. It's not a proper noun. Some people think that anything with an associated acronym requires capitalization, but that's not true.)

Also here, in a comment by Phil Radler, at Daily Writing Tips:

Arbitary CapiTALization hAs GoT tO sTOp! It’s more than just distracting, or peculiar, or annoying; in standard English, it’s plain wrong.
This error induces some of the most strident conflicts I encounter when editing; people can’t seem to distinguish between something that is appropriately capitalized due to a well-defined set of rules, and something they want to capitalize because it’s “important.” (Sorry, folks, but that ain’t the rule.) Bill Walsh has a marvelous rant on the topic in his book, “Lapsing into a Comma”; a version also appears here: . I commend it to the attention of anyone who is interested in producing well-crafted prose.