A single-celled, blue-green photosynthetic bacteria is commonly known as cyanobacteria.

While they are sometimes called "blue-green algae", this term is technically inaccurate. Algae are a diverse group of organisms that include both single-celled and multicellular species, and cyanobacteria are not actually algae.

So, the most accurate and preferred term for these bacteria is cyanobacteria.