June was a very unusual name in the IoM at that time.
The Maughold parish register has a Jane Kermeen who had three illegitimate children:
Robert Illegit son of Jane Kermeen bapt Parish Church 4 May 1856
Jane Illegit daur of Jane Kermeen bapt Parish Church 29 Jun 1858
James Illegit son of Jane Kirmeen bapt Parish Church 15 Dec 1861.

I'll see whether I can find their marriages which may have the father's name.

Sue