Because the source then goes on to name the philosophy it discusses as "logical atomism", the phrase ("should wish to") would reasonably be interpreted as "it is my goal to".
The source is essentially saying:
I'm not wrong, because I know that my logic is a singular, cohesive thing. To prove this to the people who have been criticizing it as self-contradicting nonsense, I'll call it logical atomism so there can be no doubt that it is, in fact, not self-contradicting.
In terms of action, "wishing to do something" is "wanting to do something". In terms of persuasive writing, the construction ("should wish to [do something]") may leave an impression of intellectual circumlocution, a dressing up of the argument. For comparison, my first paraphrasing of the passage possesses very little of that, but all of it can further be removed to just state facts:
People think my philosophy is nonsense because it contradicts itself. I'm renaming it logical atomism to remind them they're wrong every time they mention it by name.