The BG team was often referred to Demerara in the Trinidad press, and occasionally even the Guiana press. Indeed often both labels would be used in the same article.
And as most of the information published online so far (by Barrie) has come from Trinidad sources and the Jamaica Gleaner, i think he wrote the names of the teams as they were in the sources.
But the association was the BGFA. So it was British Guiana (de jure, at least). In practice, it is likely that the team was an effective Demerara selection, with most or all players based there. I assume the BGFA would only select players from clubs affiliated to it, which were likely all based in/around Georgetown.
Berbice had a football association, and sometimes visiting teams played there. Indeed for this 1928 series, the Trinidad team was invited there to play against an All-Berbice team, but declined due to the busy schedule they already had.
Also as SDb notes above, the colony was British Guiana (formed in 1831 by a merger of previous colonies Demerara-Essequibo, and Berbice).
Also Trinidad and Tobago were two colonies until 1899 when they were combined.
Thus to be completely strict, any "Intercolonial" match would have to be British Guiana vs Trinidad & Tobago.
However, matches are in reality played by associations (or clubs) and not countries or colonies, so other labels are possible. BGFA vs TAFA.
In some of the earlier visits (pre WW1 say) the visits were made by (or arranged by) clubs rather than associations, so in those cases there would be more freedom to choose whatever name you want.
I have quite a lot of newspaper prints from these visits but I don't really have time to go through them all in detail at the moment. Newspaper reports from this era are very long-winded (as am I) and write in small print, so they need careful reading without distractions.
If I ever do so, I will be sure to write all the exciting minutiae.
Meanwhile I could probably answer some specific questions if they are quick.