I just changed my Minecraft account name, and logged into a server to discover that my machines were locked and now considered owned by another player.

The ownership system should be using the player persistent player UUID.

Where are the data stored on the server?
A player of mine wanted to give ALL of his stuff to another player, I did so replacing his UUID for the one of his friend on all server files, and everything went to him, except Mekanism stuff.

Thanks for the report, will be fixed for next Major (breaking) version

I just had the exact same issue, just finished changing my player name to what everyone i play with knows me as and found the main item i wanted to get into (the advanced gas tank to refill my jetpack) was locked and i couldn't get into it. every other item i had before the change was still on my character

Just a heads up: I'm currently working on this issue, changing all usernames to UUIDs.
Expect a WIP pull request in an hour or so.

Done!

Any chance of getting this fixed in 1.7.10?

1.7 is no longer supported.

The UUID system or the mod
Cause the mod is still supported

Mod is supported, but not on 1.7, if you want new features go and play 1.12

Please fix the 1.7.10 mod file too

Would it really be that hard to fix the issue and make a new build?

It is not a simple change. And like has been said, we do not support 1.7