Sakashima the Impostor has the next textual content (and extra, however that is the related half):

You could have Sakashima, the Impostor enter the battlefield as a replica of any creature on the battlefield, besides its identify is Sakashima, the Impostor

Lazav, the Multifarious has considerably comparable textual content (additionally shortened to the related half):

{X}: Lazav, the Multifarious turns into a replica of goal creature card in your graveyard with transformed mana value X, besides its identify is Lazav, the Multifarious

Between these two playing cards, it is potential to have Sakashima enter the battlefield as a replica of Lazav, after which use Lazav’s capability. In most conditions, textual content on a card which refers to that card by identify is handled as “this card”, so although the creature in that circumstance is known as “Sakashima the Impostor”, activating its capability which says “Lazav, the Multifarious turns into a replica” will trigger Sakashima to turn into a replica. However, I do not know whether or not the identical applies to the a part of the power which impacts the ensuing identify as properly.

There are varied different playing cards which might have comparable results when mixed with Lazav, resembling taking the power immediately with one thing like Necrotic Ooze that I assume would work the identical manner, but when not then be happy to restrict consideration to only Sakashima.

In quick, if a creature not already named Lazav, the Multifarious has and prompts the power of Lazav, the Multifarious, does its identify change?