I also take L-theanine as a supplement.
Theanine is a chiral molecule.
It exists as two isomers.
L-theanine refers to the L isomer. There's no difference in saying that you have L-theanine or L-isomer-theanine.
As for Suntheanine vs. all the other L-theanine supplements, I personally have not noticed any difference in former brand, vs many other brands.
According to this FDA document,
http://www.accessdata.fda.gov/scripts/fcn/gras_notices/615880A.pdf only a very small amount (between 1 and 2 percent) of the theanine in green tea is D-Theanine (the other enantiomer).
I don't know why people regard Suntheanine as being higher quality than other brands, I believe this is marketing hype - if you have two products, one called 'Suntheanine' containing 100mg of L-theanine, and one called 'Moontheanine' containing 100mg of L-theanine, neither mixed with anything else, both in the same gelcaps etc, they'll do the same thing.
But whether every brand actually contains L-theanine in the advertised amount or not, is a different matter.
To be clear:
Assuming the company is honest -
There's no difference in saying that you have L-theanine or L-isomer-theanine. It is precisely the same compound, and the same that exists in green-tea.