伺う
ukagau
Why ask, hear and visit are all one verb
The picture Taking half a step toward the other person, tilting your head, and offering your ear and your foot forward together. 伺う lowers your own foot and ear and moves them closer; お聞きになる raises their act of hearing one level.
Where the picture shows up in 伺う
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half a step with one question
一つ伺ってもよろしいですか。
hitotsu ukagatte mo yoroshii desu ka
May I ask you one thing?
One question held on your fingertips as you move half a step in and stop there.
The standard opener before raising a question in a meeting.
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a blank line held out for a name
お名前を伺えますか。
o-namae o ukagaemasu ka
May I have your name?
A notebook held low and open, one empty line offered toward the other person.
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your own feet do the walking
明日、三時に伺います。
asu, sanji ni ukagaimasu
I'll come by at three tomorrow.
Your shoes set down in the 3 o'clock box of the calendar, right outside their office door.
The humble form of 行く and 来る — the default for arranging a visit.
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only the ear leans in
お話は部長から伺っております。
o-hanashi wa buchō kara ukagatte orimasu
I've heard about it from the manager.
Words out of the manager's mouth gone in through your ear and already stacked up inside you.
伺っております drops the sentence one notch further.
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a head tilted over their calendar
ご都合を伺いたいのですが。
go-tsugō o ukagaitai no desu ga
I'd like to ask what works for you.
Not touching their calendar, only tilting your head to read the empty squares.
All of it in one picture
伺う isn't three meanings, it is one half-step. Step in holding a single question and it means "may I ask"; hold out a blank line in your notebook and it asks a name; let that same foot carry you to their office door and it means "I'll come to you". Tilt only the ear and it becomes "I've already heard", and tilt only the head over their calendar and it becomes asking what time suits them.