Hmm. It would help to know who is setting this unit up, its financial backer, its political sponsor, what operations it is intended for, whether there is anything unusual about its equipment, etc. etc.. All i know about the US Navy Seals is that they are trained to board and capture ships and oil-rigs.
Meanwhile, may I float a few suggestions and see whether anything is getting into the right sort of area.
The Royal Marines.
The Duke of Albion's Maritime Regiment of Foot.
Independent Company Number One.
The Sons of Thunder.
The Small Boat Squadron.
The Murmillones.
The Favoured Sons.
The Gladiators.
The Retarii.
Popski's Private Army.
The Sacred Band.
The Okeanides.
The Underwater Highlanders.
The Scarlet Penguins.
The Orcas.