Oro Bog Liom I
I got this tune from a recording of concertina player Cormac Begley. The tune appears on Dermot Byrne’s solo album but the second part is a bit different.
Also related to the jig "My Pretty Fair Maid" https://thesession.org/tunes/1377
Thanks to Kenny and Ceolachan for their help when I was looking for this tune name !