What is the name of this fallacy: Is 101 binary or decimal?
I prefer to call it the either-or fallacy, but it is also known as false dilemma among others. The idea is that a choice is given that constrains to two or perhaps a few options when a much broader reading of responses is both possible and warranted. In your example, 101 is a number in base-2 and base-10 and every base in between and beyond.
In regards to your picture, it highlights the likely cognitive source of the fallacy, and that is ambiguity. For instance, it is ambiguous when one writes 101 and does not explicitly explain which base it is.
What's the difference between ambiguity and a false dichotomy? Well, ambiguity is a lack of context to indicate the intention of the author, whereas a false dichotomy is an argument that exploits the lack of context. To be technically precise, an argument must have two or more premises and result in a conclusion, and many logicians accept that unstated premises can be reasonably understood by context. For instance, one could posit that an either-or fallacy is essentially understood as:
P1: 101 could be binary.
P2: 101 could be decimal.
Therefore, 101 is either binary or decimal.
So, technically the question alone independent of context might not be accepted as an argument and therefore fallacy, but ANY act of drawing a conclusion regarding 101 as binary or decimal and presuming those are the only two choices is clearly a fallacy.
Note, to resolve the ambiguity, mathematicians generally use brackets or subscripts or both to indicate base. For instance _2, _10, and _16.