Nice find.
From what I can see in your pictures it does appear to read ‘BOG AMI’ (rather than ‘DOG AMI’), which is rather curious. I would think it more probably a ‘split’ word intended to read ‘BOGAMI’ in full.
It could be a surname, although not a common one. I can’t see it having any meaning in Celtic, however I read it. The only other thing I can offer is that it does have a meaning in Serbo-Croatian, either as the single word ‘BOGAMI’ or split as two words (for which the split would be ‘BOGA MI’). The literal meaning would be ‘By God’ but in the sense of either: an exclamation of surprise/wonderment; or to emphasise the impact or truthfulness of something to others that doubted it... for example:
Oh my God… (what I saw was amazing)
or
(That’s definitely what I saw)… I swear to God
The construction looks like it has at least 300 years of age to it (I have no experience of what a peat bog might be expected to do to it) and the ‘stone’ appears to be multi-coloured drawn and moulded glass of the type typically produced in Bohemia around that time or earlier. A Czech/Slovak origin would at least put us close to regions where Serbo-Croatian languages were spoken but that’s a bit of a long shot. Glass like that was also widely made in Italy too and both regions exported massive amounts of it as beads and cabochons all over Europe for jewellery-making.
