Bubble is a slave. Depersonalisation of slaves by not being interested in their name is a common form of additional control. In a sci-fi setting, you can see this in the Star-Trek Mirror Universe "Designations".
Valerian is disturbed by Bubble's enslavement, which she mistakes for displeasure at her performance. Eyes brimming with tears, she implores him to tell her what she could have done better. When she reveals her true form as a blue blob, some protean combination of the Pillsbury Doughboy and a hammerhead shark, Valerian helps her escape and it's off to the races.
It is likely that no one has ever asked Bubble her name before, hence the hesitation.
Bubble does not exist in the source material however, so there is no additional confirmation.
Vanity Fair article;
Though “glampods”—alien shape-shifters—appeared in the original comic series, Bubble is Besson’s invention.