How to share folders with a specific user on another computer

I've gone through the tutorials here on how to set up share folders. Very useful. I've done a fair bit of google searching as well. There does not seem to be an answer to my question.

I have some folders on my desktop PC that I have shared on my network using the "Everyone" group name, giving read access only (not read/write). This part is working.

FYI: I have Function Discovery Provider Host, Function Discovery Resource Publication, SSDP Discovery, and UPnP Device Host services activated in order to be able to view all my devices on the network.

I have a personal laptop that I would like to grant read/write access to the same shared folders, not just read access. I setup my account name on my laptop to be the same as my account name on my Desktop thinking this would somehow magically work, which it didn't.

How do I share a folder that has already been shared with read-only access with Everyone, with my specific user account on my laptop, giving my user account full control?

Thank you!
(currently using Windows 10, 1809 update.)

Thank you for these replies!

If I may ask for further clarification:
My desktop already has a user account (my name) with the permissions I want to the folder. Do I need to create another user account that I will never use in order to make this happen? Is there a more direct way to solve this issue?

I apologize, I realize this is probably a basic concept to most people on this forum, but what does it mean to "map a drive"?

My desktop and laptop both only have one user account created (the same name), neither of which use a password or pin. Do I need to have a password on the user accounts to make this work?

Created account should be fine. You should share desired folders with that account allowed

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I think I've tried this already, and it didn't seem to work. Using the right-click menu of the folder, I went to "give access to" > "specific people" > and typed in my account name (which, again, is the same on my PC as on my laptop). This didn't work. I noticed that the account name is specific to the pc though (DESKTOP-PC\My_User_Name). I tried specifying LAPTOP\My_User_Name, but computer says it couldn't find this user.

I've also tried going through the right-click menu > properties > Sharing > Advance Sharing > Permissions > Add, and adding or changing the location to LAPTOP from DESKTOP-PC, but that doesn't work.

The "Everyone" share is working, but again, I want to specifically give MY account on my laptop full control, whereas Everyone can have read-only access.

So what I understand you are saying is:
A) I can only map a network drive OR give access to a user but it wont work if I try to do both? Or are you saying that I only would need to do one or the other to make it work?
B) The folder that I have on my desktop that I want to give full control to on my Laptop: to do so I need to create another account on my desktop, and give that 2nd account access to the folder on my desktop. But I still don't see how that will help me share it with my laptop. It seems like I would still run into the same problems I'm having now.

I really appreciate your efforts today to help me! I'm sorry for my continued lack of understanding here.

How will this help me get full control access to my shared folders on my desktop from my laptop? My current user account on my desktop already has read/write (full control) to these folders. Creating a 2nd account with the same privileges on the desktop, and logging into that 2nd account on the desktop doesn't seem like it would allow me to access those folders with full control from my laptop.