Combine VLOOKUP and IF with specific values (and IFERROR)

Simple VLOOKUP takes the ID# and checks against Table1 (named range $B$2:$C$31) to get a name. But what I really need is whether or not there IS a name.

I figured out how to do this in two steps - by using VLOOKUP for the name,and then in the next column, testing whether it's "(blank)" - gets a 1 if it is not "(blank)"

However, when I use it against a set where the ID# doesn't exist in Table1, I still get a 1, even though it's not "(blank)" and it's not a name.
formulas in cells G5, H5, and I5:

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Thanks in advance!

I'm not looking for a specific name, just if there is a name attached to that ID#

L5=IFERROR(IF(VLOOKUP(K5,$B$3:$C$31,2,0)<>$C$3,1,""),"")

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Thank you!