Expand character space in adobe template

If you need to adjust the space but you "cannot access properties like usual", there can be several reasons. The text layer could be locked, or the text may be on a Parent page rather than the document page itself. You would need to post a copy of the file for us to figure out why you can't access the properties.

You could put the file on Dropbox, or One Drive and send us the link so we could examine it.

Perhaps the original textframe is on a parent page (formerly known as master page). Maybe it is locked or on a locked layer in the Layers panel. Find it's origin and widen its dimensions.

Another approach would be to find the paragraph style that controls that big name text and edit the style to be a little bit smaller of point size.