Both Perplexica and Perplexity are bad names for a search engine.

Very perplexed as to who was the smart person that chose this dreadful name for the company.

Yes, it has another definition in context to information theory; which my point is, I used the first definition like a normal person would, which is commonly associated with...

'...a state of confusion or a complicated and difficult situation or thing.' - Cambridge English Dictionary [0]

None of them can ever become a verb that makes sense like 'google it'.

[0] https://dictionary.cambridge.org/dictionary/english/perplexi...