Yes it's a storm now! But a it's a very small one at least. Its convection area is very small and thunderstorms appear to be quite small compared to other typical tropical storms. However at this moment thunderstorms tops are reaching FL450. That represents a lot of water that could surely cause flash floods and mudslides...
Satellite imagery showing the size of the storm and thunderstorm tops
People from Guadeloupe to Grenada should be extremely careful regarding floodings, wind gusts and also waves caused by this little storm.
AROME wind accumulation for the next 42 hours, showing gusts up to 130 km/h
And ahah yes I didn't notice that about island names :)