Pausanias referred to the worship of Artemis in Lakedaimon multiple times.

(3.10.7) The third branch from the straight road is on the right, and leads to Caryae (Walnut-trees) and to the sanctuary of Artemis. For Caryae is a region sacred to Artemis and the nymphs, and here stands in the open an image of Artemis Caryatis. Here every year the Lacedemonian maidens hold chorus-dances, and they have a traditional native dance.

(3.14.2) here is a place in Sparta called Theomelida. In this part of the city are the graves of the Agiad kings, and near is what is called the clubhouse (lesche) of the Crotani, who form a part of the Pitanatans. Not far from the clubhouse is a sanctuary of Asclepius, called “in the place of the Agiadae.” Farther on is the tomb of Taenarus, after whom they say the headland was named that juts out into the sea. Here are sanctuaries of Poseidon Hippocurius and of Artemis Aeginaea. On returning to the clubhouse you see a sanctuary of Artemis Issoria. They surname her also Limnaia, though she is not really Artemis but Britomartis of Crete.

(3.18.4) The story of Artemis Cnagia is as follows. Cnageus, they say, was a native who joined the Dioscuri in their expedition against Aphidna. Being taken prisoner in the battle and sold into Crete, he lived as a slave where the Cretans had a sanctuary of Artemis; but in course of time he ran away in the company of the maiden priestess, who took the image with her. It is for this reason that they name Artemis Cnagia.

So, in Sparta alone there were at least four different images of Artemis worshipped – Caryatis, Aeginaea, Cnagia, and Issoria (or Limnaia). According to ChatGPT, the image most likely here is that of Artemis Issoria, since it was associated with hunting, and a dog appears next to her on the coin. The others are lesser matches.

Apollo | Artemis | Dog | Magistrate | Spear | Wreath
Lakonia, Lakedaimon (Sparta)
Struck under the magistrate Timandros
Circa 35-31 BCE
Dupondius AE 26mm, 10.25g, 6h
Ε ΤΙΜΑΝΔΡΟC Laureate head of Apollo to right
Rev. Λ-Α Artemis standing to left, holding right hand over the head of the dog that is seated to the left and resting her left arm on a spear, two monograms below, all within a laurel wreath
BCD Peloponnesos 912-913. Grunaeur XIX, 20 var. (V14/R-). HGC 5, 616; NCP p.54 No 1
Ex BCD Collection, acquired January 1972
Ex collection of John Aiello