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Sami, 
I’d recommend using ‘landscape designer’ (I’ve seen this most often) or maybe even ‘recent landscape architect graduate’. If you use ‘landscape architect in-training’ check w/your state registration board to make sure that there aren’t any ‘conflicts’. 
As far as looking for jobs: the ones that generally apply to college grads would be ‘entry-level landscape architect’. Interestingly, this does not nec. mean that they want a registered l.s. arch. but that they are looking for someone w/ a l.scape arch. degree for an entry-level position.  When you check the ‘education’ and/or ‘skills’ requirements for the posted job, you will see whether they are looking for a registered l.a. or someone w/less experienced. 
If you are writing a firm but aren’t sure if they are hiring, let them know that you are looking for an ‘entry-level’ position. 
(Just for ‘kicks’, I checked the ASLA career site for ‘entry-level’ l.a. positions and found three…each w/a different ‘call-out’ for the position: graduate l.scape arch., entry level l.scape designer, and l.scape designer. None were looking for a registered l.a.)