Complex sentence: This event did indeed occur, in the Norman Petty studio in Clovis, New Mexico, but it did not inspire the Crickets to choose the name: it happened after they had already decided on using the name the Crickets.
Split into simpler sentences: This event did indeed occur, in the Norman Petty studio in Clovis, New Mexico, but it did not inspire the Crickets to choose the name. This happened after they already decided on using the name the Crickets.