Walter Muir, married to Janet McIntyre, died in Shotts in 1917.
So it looks as if Margaret was illegitimate, hence the register recording two surnames for her.
I speculate that Laurie is the name of her biological father.
An illegitimate birth can only be registered under the father's surname if he accompanies the mother when she goes to register the birth, and signs the certificate along with her.
If the father doesn't do this, it's not uncommon for the mother to give the child its father's name, in this case (probably) his surname as a middle name.
If a court of law finds that a certain person is the father, this creates a record in the Register of Corrected Entries (RCE) to that effect, but the original certificate is not altered.
The child can use any surname it likes it later life.