Hi,
Very sorry for been so late regarding this post but have only just discovered the site.
Regarding your Grandfather being down as belonging to 8th (Leeds Rifles) Battalion The West Yorkshire Regiment, that would be correct as his parent unit and cap badge. As to serving with a different Regiment again most likely and quite common after the armistice as certain Battalions were earmarked for Army of Occupation duties whom needed to keep their manning levels up as soldiers were being discharged at the end of their commitment, so as an officer or soldiers unit who still had a service commitment was reduced to cadre/drawn down and returned to the UK they would be posted to another Battalion not necessarily of their own parent cap badge. It would seem that the norm in such cases would be for officers to retain their parent unit cap badges whilst other ranks were re-badged to the new unit. Some unit war diaries for late 1918/1919 document these cross postings well, unfortunately some don't.
Regards,
Stateside 123