。
The lost girl sobbed as she said her name.
Literal
Lost-child [possessive-の] girl [topic-は] sob [while-ながら] name [object-を] was-saying.
~ながら ('while X-ing') is the standard Japanese frame for simultaneous actions, attached to a verb's masu-stem. The subject of both actions must be the same. すすり泣く ('to sob, to weep') is a compound verb built from すする ('to slurp, sniffle') + 泣く ('to cry'). Vivid and specific.