Sorry for being so slow in responding. If you look at my reply to a previous comment it seems difficult to avoid a conclusion that there was something odd which may amount to fraud but I can't see a motive for a fraud where it was transparent - if something criminal was going on I assume one or other of the names would be used but not both.
The names were
Father - Daniel Cooper Thomas
Birth certificate - mother Sarah Thomas formerly Cooper whom he married in 1856.
Baptism mother - Harriet Thomas who he married in 1825.
Date of birth - 12 Jan 1849
Registered - 22 February 1849
Baptised - 25 February 1849
Bigamy seems to be ruled out; if he was co-habiting I suppose it's arguable that he would have been more careful of the church than the law.
As a matter of record 5 children were baptised at the same time with birth dates ranging from 1831 to 1849 - the first I assume because she was getting married and needed to be baptised for a church wedding.
If this helps with your thoughts, I'd greatly appreciate it.