(1) That's a big part of who I am.
(2) When that day comes if you don't like who you are, you're done.
At first blush, the who's in (1) and (2) seem to be relative words in the fused construction.
CaGEL* (Page 1077), however, seems to say that both these are interrogative pronouns. Specifically, CaGEL says this:
An example of the free choice construction is:
Invite who you like.
And I don't think the boldfaced expression in (1) or (2) is the free choice construction.
Does this mean that the who's in (1) and (2) are interrogative pronouns?
Here's what CaGEL (Page 1076-77) says about 'how' marginally occurring in a fused relative:
Examples with how are found but they are rare and quite marginal:
%We will not change how we use future contracts during the term of this Prospectus; %I don’t like how it looks.
These examples are construed by CaGEL as possible -- admittedly marginally so -- cases of how occurring in a fused relative.
Now, returning to example (2) above, I don't know why you don't like who you are should be interpreted differently than I don’t like how it looks. That is, if the latter's how is construed as a fused relative word, albeit marginally, then why shouldn't the former's who be?
*The Cambridge Grammar of the English Language by Huddleston & Pullum