This is dedicated to Bethan and Manon. Dw i’n ddiolchgar byth a hefyd am eich help chi gyda’r iaith.
A brief look at the Welsh word for Wales: Cymru
This has been a subject I have thought about writing many times in the past, and I’m glad I finally have.
Cymru derives from the Brythonic, or early Celtic, word combrogi, which meant “compatriots”. This makes Cymru (Wales) “land of compatriots”. This in turn comes from an earlier Celtic form combrox, which probably came from an unattested form, *kom brogos. The first part of the word, *kom is a collective prefix from Brythonic, probably related to Latin “com”. We can see plenty of examples in English today, such as “compatriot”, mentioned above. The second part, *brogos meant “area, district”. It may have come from a Proto-Indo-European root, *merg, meaning “boundary, end of territory”.
I shall look at the English word, Wales, at another time.
Glossologics 
The Welsh ‘-bro’ element of the earlier Celtic form ‘combro(x)’, being a word on its own meaning ‘country’ in the Brythonic branch of the Celtic languages:
Welsh: ‘bro’ – land, region, vale
Cornish: ‘bro’
Breton: ‘bro’ – ‘country’
can be traced back through British *brogh, *brog to a Common Celtic *mrog.
From the same Celtic root on the Goidelic branch are
Irish: ‘brú’ (brink) ‘bruig’ (boundary)
Scots Gaelic: ‘bruach’ (bank, brink)
Manx: ‘broogh’ (steep bank)
All these I think can be tracked back to a Proto-Indo-European *bhru- (edge/rim/brow/border) cognate with:
English: brow
Old English: bru (eyebrow)
Ancient Greek: ὀφρῦς (ophrus, “eyebrow”)
Lithuanian: brùvē (“brow”)
German: Braue
Old Norse: Icelandic: Faeroese: brún
Norwegian: brun
Swedish, Danish: bryn