Ram Dass (dāsa=devotee (of Lord Rama)).

You might have known other people with similar last name (eg: Anil Dash).

The most common pronunciation is "Das"

Why does anyone feel the need to take on a new name just because you change your religion? I never understood that. I have had epiphanies that dramatically changed my world-view, but I never thought "Now I must take a new name". I'm not criticizing those who do this, since people change their names all the time anyway, but I'm genuinely curious why this phenomenon is so common when people change their religion?

This is what I understand - in the Hindu tradition (perhaps it's similar in Buddhist and Catholic traditions) you are supposed to enter a new life when you become a Sannyasi (monk). One of the initial rituals in many schools is to perform funeral rites for your former self. Through this process, you renounce your family, relations, and what you think of as your "identity". Then the guru gives a new name to the monk. Afterwards, monks are prohibited from talking about their purvashrama (previous life).

It's part of losing your old identity. You are no one. So join this ashram and till my soil while I sleep with everyone. It's a cult tactic.

You'd use a new title if you switched trades. How is this any different?

Sometimes it is a tribute to a great figure

He should have spelled it "DAAS" instead of "DASS", because DAAS is how it's supposed to be pronounced.

There's no universal way to pronounce given letters, especially when transliteration is involved. Neem Karoli Baba chose the name for him. Not sure how the spelling was decided upon, but it seems pretty trivial, as spellings/pronunciations change all the time.