Is there any adverse consequence by changing trainer's name?

I am playing pokemon Y (not yet cleared) and Alpha Sapphire (first clearance). I used pokemon bank once and I believe I did not register PGL (in case it matters).

It's my intention to change trainer's name by using PKhex and I wonder whether by doing so it would mess up the game. I gave a search on google but not much info on this point. Any response to the following is grateful:-

1. Would change of trainer's name affect the legality of the pokemon I caught so far?

2. Do I have to generate a new Trainer ID as well on top of the change? Are there any other follow-up actions that must be pulled off?

3. Do I have to change every Pokemon's info as well so as to make it obey to me? What would happen if I do not do that? (I suppose they would merely disobey my order, but this could be solved if I clear the game once).

4. Would it mess up the game in other aspects? Like the name other people call you in the game, or is there any other adverse consequence that may occur?

1. Would change of trainer's name affect the legality of the pokemon I caught so far?

As long as the name is legal it should not affect legality in any way.

2. Do I have to generate a new Trainer ID as well on top of the change? Are there any other follow-up actions that must be pulled off?

No other actions should be needed.

3. Do I have to change every Pokemon's info as well so as to make it obey to me? What would happen if I do not do that? (I suppose they would merely disobey my order, but this could be solved if I clear the game once).

A game clear will make any Pokémon (Bred or traded for) obey your orders.

4. Would it mess up the game in other aspects? Like the name other people call you in the game, or is there any other adverse consequence that may occur?

There should be No issues with it.

As long as the name is legal it should not affect legality in any way.

No other actions should be needed.

A game clear will make any Pokémon (Bred or traded for) obey your orders.

There should be No issues with it.

May I know the source? Did you try change name by yourself or?

I changed my trainer name before and as far as I can tell there was no harm and everything Odaxis said is correct. You'll have to update your pokémon's OT though to make they be treated as yours.