“Going Full Monzo” is just the nick name given to people who use Monzo as their main bank account (so having their salary going into it, direct debits coming out, using it for day-to-day spending etc).
“Full Monzo” as a ‘product’ doesn’t exist - it’s just ‘normal Monzo’ being used to it’s “full” potential.
So, yes, your existing Monzo account is fine to have your Pay going into it and (since Monzo is your only bank account) you’ve already “gone” full Monzo! Congratulations! 