numbers join two columns WITHOUT a space?

From your screenshot it does appear that you have a space before the D in Down. That would account for the space you're seeing in the results of your formulas.

SG

I've tried to replicate with CONCATENATE and &. No mystery spaces here.

So I suggest double-clicking that Down cell to edit it, moving the cursor one space to the right with the right arrow key, hitting the delete key, and then hitting return. That should remove what really does appear to be a space before the D. (You can see it because the D is not next to the left border of the cell the way the R is in its cell.)

SG

If there truly is no space in there, then make sure your 'lastname' column has a Data Format of Text, not a Custom Format with a space before the text.

This:

Not something like this:

SG

you can also try:

=substitute(left(B2, 1)&C2, " ", "")

which will concatenate the left most character in the cell B2 with the contents to C2, then substitute nothing for all spaces

This statement is counter to common expericenes.

Please save the work you have and email the file to me. My email is in the bio of my profile.

Also try creating a new document and repeating the steps.