Should English be renamed?

I suppose that if I had to rename the English language, I'd call it Britannic, since it is largely a fusion of two languages that came into form in the British Isles (Anglo-Saxon and Anglo-French). However, I'm sure that Celtic-speakers would resent such a name change, especially since there are very few instances of Celtic influence in English. All in all, I would not advocate a name change.

<<I'd call it Britannic, since it is largely a fusion of two languages that came into form in the British Isles (Anglo-Saxon and Anglo-French)>>

Not exactly.
The English *lexicon* can be thought of as a fusion of Anglo-Saxon and Anglo-Norman on certain levels (upper tier 1 and tier 2 registers), but the language as a whole? definitely not.

English is Modern Anglo-Saxon with borrowings (overlay) from Norman and French.