How to rename the User folder in Windows 10?

This can be done without folder renaming and messing with registry:

Create a local account with the user name you wish.
- Local account creation is well hidden; here is how to find it:
  Settings > Accounts > Family & Other users > Other users > Add someone else to this PC > The person I want to add doesn't have an email address > Add a user without Microsoft account
Change account type to administrator (can skip if there is other administrator).
Remove original Microsoft linked account
Link local account to Microsoft account if you wish

Microsoft has actually documented a very simple and clean way to rename a user profile folder.

There is no need to create a new user account, so all the settings associated with the existing user profile are preserved. And the only registry change required is to edit a single string value (the one that tells Windows the path of the user profile folder):

Log in by using another administrative account.

Note You may need to create a new Administrative account at first.

Go to the C:\users\ folder and rename the subfolder with the original user name to the new user name.

Go to the registry and modify the registry value ProfileImagePath to the new path name.
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\ProfileList\<User SID>\

That's it!

The procedure quoted above was provided by Microsoft (here) in relation to a perceived issue with Windows 7, and continues to work in Windows 10.

Notes

<User SID>

The ProfileList registry key contains a number of sub-keys. To find out which one to change, click on each sub-key and examine the values, to find the sub-key with the right ProfileImagePath:

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For example, let's say we want to get rid of the space in a user profile folder name. So in step 2, we use File Explorer to navigate to C:\Users and rename the John Smith subfolder JohnSmith. And in step 3, we click on the <User SID> sub-keys until we find the one with ProfileImagePath C:\Users\John Smith, and change it to C:\Users\JohnSmith.

Administrative login

You may find you have to restart instead of just logging out and logging back in. Otherwise, when you try to rename the folder, Windows may report that it is being used by another program.

Environment variables (info)

Some applications create env vars with the user profile path fully expanded, so it's advisable to check for these and reboot if any needed fixing.

While not a direct answer to the question, a symbolic link can be a risk-free solution if the problem is not just aesthetics, but that restored or legacy configuration files or links refer to the user directory.

Open an elevated command prompt
Change to the user directory
Create a directory junction targeting the real name of the user directory

e.g.,

C:
CD\Users
MKLINK /J Jeremy jerem

This enables you to use c:\Users\Jeremy\..... to refer to parts of your profile.

I had the same problem and I have solved it as follows (using information that I found on a few other websites):

Just to be safe, create a restore point. Open the Control Center, type in System Restore and click on Create System Restore Point. Select the C: Drive and click on Create.
Click on the Windows Button (at the bottom left), type regedit and click on Execute command.
Confirm the UAC dialog by clicking Yes.
Make a backup of the prior registry by clicking File > Export.
Go to HKEY_LOCAL_MACHINE/SOFTWARE/Microsoft/Windows NT/CurrentVersion/ProfileList. There you can find a few subfolders (starting with 'S-1-5-'). Search for the folder that contains the path (that you want to change) in the registry key named ProfileImagePath. (Example from the question: search for the value 'C:\Users\jerem').
If you have found it, double-click on it and change the path. (Following the original question, you would now change the value to 'C:\Users\Jeremy').
Close the Registry Editor window.
Click on the Windows Button (at the bottom left) again and type netplwiz and click on Execute command.
Make sure that the checkbox 'Users have to enter username and password' is checked. Select the user (for whom you want to change the path) from the list and click on Properties.
Change the user name in the new window. (Following the original question, you would now change the user name to 'Jeremy'). You can also change the full name here, if you wish (but in my case the correct name has already been entered). I suppose that you can not leave the full name field empty. Close the window by clicking OK.
Close the other remaining opened windows also by clicking OK.
Restart the system.
Start Windows 10 again and try to login. This will fail (because of the changed path) and you will automatically be logged in with a temporary user account (which will take a bit of time). However, you can now change the name of the folder using the Windows Explorer (following the example above, you would now rename the folder jerem to Jeremy).
Note: alternatively, you can boot into a second operating system (if you have one installed) or use a Live CD operating system to change the folder name.

UPDATE: Thanks to user @lmiguelvargasf for informing me about an issue with my solution! I thought that the system would be a bit more intelligent in updating the references in the registry, but it is not! Therefore you should start the Registry Editor again (as in step 2) and make a backup by clicking File > Export. Then click on Edit > Search (or Find...), type in the old path (in the example it would have been C:\Users\jerem) and search for keys, values and data. Replace all references containing the old path (C:\Users\jerem) with the new path (C:\Users\Jeremy). A click on the key F3 searches for the next reference. Repeat that until you don't find any references to the old path. Even with a relatively fresh installation on Windows 10, you might have to update about 100 entries (especially OneDrive and Edge have quite a lot of caching paths in the registry). And also some additionally installed programs might have created registry entries!

Finally, restart the system again and start Windows 10. The first login could take quite a while, but everything should now work fine again and the path of the user directory should now be changed! If everything works fine, you can now delete the original folder (the folder named jerem, using the example of the question).

INFO: I am working on a German system. I tried to translate the bullet points correctly, but it is very likely that they might be named a bit different!

DISCLAIMER: This solution is working on my laptop after upgrading from Windows 8.1 (64-bit) to Windows 10 (64-bit). However, I cannot guarantee that this solution might also work for others with other configurations. If you follow the solution provided above, you are doing everything at your own risk!

To access the Advanced User Accounts panel type netplwiz in Search the web and Windows box next to your Windows button then click or tap on Netplwiz (Windows application).
In the Advanced User Accounts panel, select the user you want to modify and click Properties
In the properties window for the user, enter the new user name and click OK.
Restart for the changes to take effect.