If I block someone I've messaged and change my tag, will they be able to see I've changed it?

Someone messaged me over live and my friend replied, turns out they're creeps and when I block them another account tries to add me on their behalf.

If I block them and change my gamertag, will they be able to see on the previous messages that were sent to them that my name has changed?

This is on 360 by the way.

:)

 

My account

Hey there. I was at work and a friend messaged me on Twitter asking me why I had changed my name and removed all my friends. I got home from work at 6 am and my gamer tag had been changed. Someone had gotten on my account, and changed my gamer tag and
removed all friends. I've called Xbox support, apparently there is also a ban on my account. I've changed all security proofs. However they can't refund me that money. Is there anything I can do to help with this? Or am I going to have to stick with this gamer
tag until I can purchase a new one? Feel free to ask any questions if I made anything unclear. Thanks

 

Gamer pic changed on its own.

Hello, my gamer picture recently changed on its own and i'm wondering if there's any way to find out if it was changed by microsoft, a glitch or "myself". I'm worried someone may have hacked my account as this came at the same time
a hacker i met in an online match messaged me about game sharing. I don't know why someone would only change my picture if they had access to my account but i haven't received any messages on my xbox one or its assigned email that i've violated any gamer picture
rules.

 

I believe so unfortunately D:

 

Yes. They will see your new gamertag if they saved the messages they send to you.

 

Well that's annoying.

Is there any way to stop these freaks from having a different account add me after each one I block?