Given information:
Central atom = X
# lone pairs on X = 2
# bonds by X = 2 i.e 2 X-Y bonds.
The structure can be represented as Y-:X:-Y
It can be abbreviated as XY2Z2 where Z2 represents the two lone pairs on the central atom X.
Based on the electron geometry which accounts for the 2 two pairs and the 2 bonds, the central atom X would be sp3 hybridized with a tetrahedral geometry
From a molecular geometry perspective (which does not consider the lone pairs), the structure would be linear.