If it is in bloom then Trichodesmium otherwise look like Oscillatoria. Please confirm identification with the the specific movement normally observed in Oscillatoria. Further, in Trichodesmium, red pigment will ooze out from phycoerythirn when incubated for long in saline water.
Confirm with the 16S rRNA gene sequence analysis. Marine cyanos are very well represented in the sequence databases (unlike terrestrial soil phylotypes), so you should get id to species level.
Apparently, it could an Oscillatoria. Trichodesmium form colonies and it is not the case. Of course a 16S rRNA would be very valauable to adscribe genus and specie.
You may find the publication by Jiří Komárek & Jaroslava Komárková (2005) helpful with the classification of these planktonic members of the Oscillatoriales; described as belonging to the Phormidiaceae. A review of the literature is also presented with a discussion concerning the separation of the genera within this family that makes use of the latest findings concerning their ultrastructure, life strategy, phenotypic appearance, and separation according to molecular 16S rRNA sequencing. As you will see, its complicated.