Could it be a version of Teignyeo perhaps?
The last two letters of the place name in the baptism entry are "ow".
The letter before it COULD be a 'y'.
The word 'Yeo' is pronounced 'yow', with the 'o' pronounced as a capital 'O', (Yo). (I've lived in a place with 'Yeo' as the place name!).
The rest of it is actually spelt
'Teing' - the 'n' coming before the 'g' as you would normally get in 'Teign'.
Whether this is just a slip by the vicar is anybody's guess, but it would mean a pronunciation more like 'Ting' than 'Teen'.