Hi Nebo,
You are correct, the LeadName field doesn't show up in the Customers or Contacts tables, if you seeing this value from the New/Edit Lead Screens, note that this is only a label, not the actual fieldname stored in the table. I am not sure how familiar you are at this point doing customization in Method, but I can give you a bit of a tip moving forward when you have to figure out the actual Field Name for fields with a custom label. What you can do is create a copy of the screen where this value is that you are looking for (Because we aren't doing any editing of this screen, make sure to make a copy but not replace any tablinks, and no need to add this to an existing tab). Once you have loaded the screen in the Method Screen Designer, you can right-click in the screen designer area and choose the option "Show Summary", as shown in the screenshot below. This feature will show you a summary of the screen, even better this summary info shows you the "Caption" name (aka label) for the field and in the next column, the actual table field name.
I took another screenshot, shown below, of what shows up after selecting the "Show Summary" option:
The examples I am showing here are actually for the New Lead screen, so I believe this is the information you are looking for anyways. So, if you look at the above image for the Lead Name caption, it shows the actual table field name is "Name" (if you look at the top of this screenshot, you will see this screen is based off the Customer table). One last piece of information I can offer you here, is I recently wrote this blog post, explaining how to import Customers/Contacts/Lead into Method. This might be helpful for you, because I outlined all of the necessary/required fields here, but I also discussed some other required field names are that might be labeled/Captioned differently on the actual screen. I hope this has been helpful.
-Ben