From the BBC article about the announcement:
All ideas will be put before an expert panel and it is they who will make the final choice.
the competition website is here.
From the terms and conditions of the contest:
The UK Space Agency will appoint a judging panel. That panel will select a winning name from all the names submitted. The decision of the panel of judges (acting reasonably) will be final. If more than ten entrants submit the same winning name, 10 entrants will be selected at random from those with the winning name.
As part of their decision, the panel will consider whether the name is acceptable to all ESA Member States.
A list of names of the judges can be viewed on the UK Space Agency website from the Closing Date for a period of 30 days.
You agree that the Promoter may, but is not required to, make your entry available on the UK Space Agency Website and any other media,