Say, my son is 3 now and I show him a clip of him/himself (not sure him or himself) when he was 1.
I point to him in the clip.
Should I say "That is baby Tom" or "That is Tom baby"?
Here you are using 'baby' as an adjective so it must go before the noun. The noun here is 'Tom'.
So "That is baby Tom" is correct.
Another option you have is to use 'baby' as a noun like this: "That is you as a baby" (If you were talking to a third person: "That is Tom as a baby")
Using "you as a baby" would avoid referring to your son in the third person, although since it is a young child, this may not be necessary or preferred (the preference would be up to you based on how you normally speak to your son). If you were talking to or about an older child or adult, "you/Tom as a baby" would be more appropriate in most situations.
Sidenote: Where you have asked about him/himself, himself is the correct choice.