Is there a way to label the centre of the new reference grids with the grids name? as below.
If no way to directly label, any method of turning the grid into a attributed polygon layer I can label in the map view?
Consider using the Grid Index Features geoprocessing tool instead. I get the feeling the reference grid you are using is simply a graphical aid, so isn't meant to be turned to a polygon that can be labelled. Grid Index features are the polygon equivalent.
https://pro.arcgis.com/en/pro-app/tool-reference/cartography/grid-index-features.htm