Model deep in trouble checks how to change name (4,4)

I haven't cracked this one yet — but the brilliant team at Fifteensquared have:

I’m struggling with the wordplay here. Possibly an anagram (in trouble) of DEEP , inserted into DOLL (a model of a person), but the word order is a bit confusing; “checks” can mean “restrains” but I’m not sure it makes sense as an insertion indicator. Any better ideas?