Would a sentence like "How do you know me?" have the inchoative aspect? I think "how" in this instance means "method, way" but it bothers me that the sentence is present tense if it does have the inchoative aspect where "know" means "to enter the state of knowing." If it is the inchoative aspect, why isn't it past tense if something like "how did you find out who I am?" is the proper way to put it? Given the definition of "how" here, I don't think it works without the inchoative aspect, but I can't explain why it's present instead of past tense.
In your example question, "how do you know me?", 'know' might be used as a stative. In context, it might not be inchoative, because it might not express the beginning of the state of knowing. The answer to the question might be "as a friend", or "by your distinctive walk". For example, consider this exchange:
"I know you when I see you."
"How do you know me?"
"Your funny way of walking and your 3 meter height are usually the first clues."
When "how do you know me" is an idiomatic shortening of 'how did you come to know me', where the past tense is conveyed by the elided verb 'did', then 'know' is inchoative, but the form remains stative.