It's probably not a floating crane as such, but a barge. The crane has crawler tracks, so can be driven on or off as required. A floating crane has the crane permanently mounted on the vessel.

Can't see a close match of any on the site. The vertical added steelwork bars around the hull seem quite distinctive.

Although the crane is a "Lima 2400", it is not the same one as on IOANNA or ANASTASIA

Why not just email the company?

Logo of Christopher D. Konstantinidis on her (http://www.constantinidis.org/equipment/dredgers/) but which one ? What do you think ?