What's the etymology of this term in basketball, that an assist is called a dime? I tried looking up on google but I didn't find any satisfactory answers.
There isn't really a verifiable source on this, unfortunately, without perhaps doing a ton of research of old television announcers. I've never seen that.
What I have found so far, is that it likely dates back to urban slang, popular on the east cost (Philadelphia and environs, most commonly attributed), which described "assisting" the police in an investigation as "dropping a dime". That was due to the cost of a pay phone call back then - $0.10 - which would be used to call the police. That apparently transitioned to assists in basketball. Wiktionary shows these meanings, for example, and all sorts of online discussions support this - but nothing meaningful as proof unfortunately.
It's also possible that it simply was directly related to the cost of a phone call, of course. The other terminology is fairly similar; a successful pass to someone that then scored off of it might be called "connecting with" that someone, for example, identically to if you connect a phone line. You feed them, same as you feed a pay phone dimes. There are a lot of small similarities that might either have been the initial connection, or reinforced it once it was made by someone.
The term "dropping dimes" in basketball refers to an "assist". A player does a lot of hard work, drawing multiple defenders to himself/herself, then passes the ball unselfishly to a teammate for an easy score. The passer is credited with an "assist" for this effort. The term in question seemed to have originated by persons "dropping dimes" to homeless persons to make a phone call if needed, as pay phones at the time cost 10 cents. Sadly, this form of charity was often done in a derogatory fashion as 911 calls are free. In a lame attempt to be "cool" and creating useless slang, somebody started to refer to high quality "assists" in basketball as "dropping" teammates "dimes", or high quality passes to them leading to easy scores. A more noble basketball charity of sort. "Raining dimes" are players that amass a lot of assists in a single game, often done very creatively and unselfishly. A "great pass", or a more creative "no-look pass", which leads to an easy score for a teammate is scored as an assist, but those terms apparently are not "cool" enough, so "dropping dimes" was born, sadly. I hope that helps.