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This entry does indeed say 'Julian Connor'
Perhaps a spelling of Julia or Julienne.
There is another 'Connor' name mentioned in the entry - presumably one of the witnesses, but this clerk loved his abbreviations, and it's tricky to make out the first name of this witness.
They would quite probably have been a relative of the bride.
Whatever this first name is, it's the same as the first name of the second witness - somebody Hanlan or possibly Harlan.
The name could be Jer(emia)h?