A name for the sound of liquid discharging from a bottle into a glass

You can try glug.

glug (ɡlʌɡ) n
a word representing a gurgling sound, as of liquid being poured from a bottle or swallowed

Gurgle

Make a hollow bubbling sound like that made by water running out of a bottle.

Gurgle (Oxford)

Definition from Google. I like this word, it sounds a little less vulgar than glug.

burble verb 1. make a continuous murmuring noise. "the wind burbled at his ear" synonyms: gurgle, bubble, murmur, purr, whirr, drone, hum, rumble "two fountains were burbling outside"

I personally would probably use the word cascade.

Verb 1. (of water) pour downward rapidly and in large quantities.

Usage examples::

• a."water was cascading down the stairs"

• "rain cascaded from the roof"

synonyms: pour, gush, surge, spill, stream, flow, issue, spurt.