No, it would not have been sufficient 2020 Lets not do it again toilet paper Christmas ornament to know his “human name”. While both names refer to the same object, The Death Note requires some specifics in order to work properly. Just knowing a name is not enough (as pointed out in the first few episodes of the anime) because one might kill another person by mistake, by thinking of a completely different individual who goes by the same name.
If it were possible, Light wouldn’t 2020 Lets not do it again toilet paper Christmas ornament have had to come up with an elaborate plan for eliminating L. He could’ve just written his name (L) and imagined him, leading to L’s demise. Light wasn’t able to achieve that, and he couldn’t figure out a way to establish L’s identity even when working on the inside of the HQ (which is why he relied on Rem’s involvement).