OK, to be exact, the below mentioned legions have been formed by the Romans as follows:

Before Caesar:
Legio VII Paterna Claudia Pia Fidelis
Legio VIII Augusta Pia Fidelis Constans
Legio IX Hispana Triumphalis
Legio X Equestris Gemina

Caesar, 58 BC:
Legio XI Claudia
Legio XII Fulminata Antiqua Certa Constans

Caesar, 57 BC:
Legio XIII Gemina
Legio XIV Gemina Martia Victrix

Caesar, 52 BC:
Legio V Alaudae
Legio VI Ferrata

Caesar, 49-48 BC:
Legio I Germanica
Legio III Gallica
Legio IV Macedonica Flavia Felix

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Then:
C. Vibius Pansa, 43 BC (consul):
Legio II Augusta Sabina
Legio III Augusta Vindex

Marcus Antonius (as triuumvirus):
Legio III Cyrenaica
Legio IV Scythica

C. I. Octavianus Augustus, 41-40 BC:
Legio V Macedonica
Legio VI Victrix
Legio X Fretensis
Legio XV Apollinaris
Legio XVI Gallica Flavia Firma

C. I. Octavianus Augustus, 30 BC:
Legio XX Valeria Victrix
Legio XXI Rapax
Legio XXII Deiotariana

Caligula, 39 CE:
Legio XV Primigenia
Legio XXII Primigenia

Nero, 66-68 CE:
Legio I Italica
Legio I Adiutrix Pia Fidelis

Domitian, 83 CE:
Legio I Minervia Pia Fidelis

Trajan, 105 CE:
Legio II Traiana Fortis
Legio XXX Ulpia Victrix

Marcus Aurelius, 168 CE:
Legio III Italica Concors

Septimius Severus, 197 CE:
Legio I Parthica Severiana Antoniniana
Legio II Parthica Felix Albana

Thus, as You've said, the "Republican" legions can be named those formed before the Caesarian civil war, up until 48 BC.