You would no longer have the Verizon account - despite being owned and powered by Verizon's network it is a separate entity - just as if you switched to any other carrier.
However, take some time to read the experiences here in switching from Verizon to Visible... and thoroughly understand the differences. Do your homework. The following will get you started:
https://www.androidcentral.com/visible-vs-verizon-wireless
