I read it as follows:
When she went to register the birth, she gave her proper name, say Mary Jones, but pretended to be married to John Jones, master mariner, when in reality her sister was married to John Smith, chemist.
I have not come across such a registration in my lot, though there are a couple of invented fathers on marriage entries.
However my lot were not exactly "middle class", so less likely to be swayed by "respectability".
I'm not sure why she would bother. The registrar would see dozens of illegitimate births. If he knew the family then he would be aware of the lie. If he didn't, it wouldn't matter anyway, unless they lived in a part of town which was known to be very "straight-laced" and the registrar was prone to gossip.
Then again she may have been considering the future life of the child. The invented father could easily be "drowned at sea" and the child would have a certificate to show later in life without a hint of illegitimacy.