So how do names work in LCS/EU LCS?

I've always wondered how professional players get or keep their summoner names in professional tournaments or teams. It's hard to find the words or for me to explain my thinking. So let's use my summoner name for example, 0neHer0, and I get put into a professional team somehow. Let's say I join a team called ROB (Rock On Bro) for example, haha... Would my name be ROB 0neHer0 or ROB Hero? Would I or someone have to buy a summoner name change for me? Would I have to create a new account? Would it be acceptable if I wanted to make a new name up that's either totally different or somewhat similar that's not taken?

Hopefully you could understand or relate to my thinking. Much respect to the LCS and EU LCS proffesional players out there!