Going by the commonest references in Ancient Greek literature and the closest associations in Ancient Greek religion, the best candidate for this particular hymn's addressee would appear to be Rhea, but specifically as filtered through her identification with the ambiguous Phrygian deity Kybele [Cybele] (or a perhaps pre-Hellenic goddess who would become identified as Kybele a couple of centuries after the Homeric Hymns' composition).
The musical and wilderness aspects, together with the lions, of this hymn are signature attributes of Rhea-Kybele, eventually finding their sharpest focus in Nonnus' Dionysiaca (see also Orphic Hymn 14, & cf. Orphic Hymn 27). Likely based on such evidence, Theoi.com evidently takes it for granted that the hymn is in honour of this divinity, listing it as one of the "Hymns to the Meter Theon {Mother of the Gods}" at the end of its "Rhea-Kybele Myths" webpage series.
This notwithstanding, there is a lot of conflation and syncretism of the most prominent goddesses, i.e. Gaia, Rhea, Demeter, Persephone and Hera, which occurs in Ancient Greek religion, which is expressed in some of its mythology, and which may or may not be a result of the identification of these goddesses, being either important maternal or chthonic figures, with the Great Phrygian Mother, whom the Greeks would call Kybele, but also simply "the Mother of the Gods."
In her 1999 book In Search of God the Mother: The Cult of Anatolian Cybele (University of California Press), Lynn Emrich Roller notes (p. 170) that the Derveni Papyrus (Col. 18, Line 7) explicitly says that:
Ge [Gaia, "Earth"] and Meter ["Mother"] and Rhea and Hera are the same thing.
Roller goes on to tell us (on pp. 174-175) that
Pindar addresses Demeter as the goddess with resounding cymbals, using
the imagery of Meter, and the fifth-century B.C. poet Melanippides
states explicitly that the two goddesses were regarded as identical...
(Melanippides says that Demeter and the Mother of the gods are one).
The Derveni Papyrus makes the some claim, stating that Demeter
received her name Γῆ Μήτηρ because she was a fusion of both
goddesses.
So the Meter in the earlier Derveni Papyrus reference appears to be equivalent to both the enigmatic "Mother" deity and to the less shadowy goddess Demeter.
On pp. 170-171 of her book, while observing the identification of the Phrygian Mother with Gaia, Roller explains why Rhea became the more vivid counterpart to the great Anatolian goddess.
The concept of Mother Earth, however, seems to have been a fairly
abstract one to the Greeks. Mother Earth was only rarely represented
in Greek art, and is usually shown as a mature woman rising up from
the ground. She was not the goddess with tympanum and lions.
More concrete is the figure of Rhea, the wife of the Titan Kronos, who
also figures prominently in Hesiod's Theogony...
In the mid sixth century B.C., the Greek poet Hipponax equates Kybele,
the Anatolian Mother, with Rhea, the Mother of the gods. By the fifth
century B.C., this syncretism had developed to the point where the
cult figure Meter could be addressed as either Kybele or Rhea: In
tragedy, both Kybele and Rhea use the tympanum and were at home in the
mountain environment.
On pp. 169-170 of Roller's book:
It has long been recognized that the Greek Meter was a highly
syncretistic deity, embodying not only an Anatolian predecessor but
also traits of a Hellenic or pre- Hellenic Mother Goddess. The
Classical goddess was both Μήτηρ, Meter, the Mother, a direct
transfer from her Phrygian cult name Matar, and also Μήτηρ θεῶν, the
Mother of the gods—that is, of the Olympian pantheon. This dual
identity caused the Anatolian Mother Goddess to become conflated in
Greek literature and cult practice with other Greek mother deities,
each of which would contribute to her personality and to her identity
in the perception of both Greeks and Romans. As the Mother of the
gods, she was identified with Gaia (Earth) and, more especially, with
Rhea, wife of Kronos and mother of the six original Olympian gods. As
Meter, the Mother Goddess, she became closely allied with the Greek
deity who exemplified motherly devotion, Demeter. The fusion was never
complete, and the constituent deities who formed elements of Meter
during the Classical period were recognized and often addressed as
separate entities. Yet the separate elements of Meter's personality
were no longer distinct either, and the assimilation of Meter with
other figures such as Gaia, Rhea, and Demeter only underscores how
widely the syncretism had progressed and how much the character of the
Anatolian Mother had come to influence her Hellenic counterparts.
One aspect of Meter’s identity was as Mother Earth. Earth, Γῆ or Γαῖα
in Greek, the Mother of all life, was already a potent figure in
Hesiod’s Theogony. Not only did she symbolize the agricultural
fertility of the land, but she was also, in Hesiod’s poem, literally
the progenitor of all beings, divine and human.
With Homeric Hymn 14 aimed at the Phrygian Matar or to her Greek interpretation of "Kybele," it would be a short step to saying that the Mother of whom you ask is (mostly) Rhea, but also, sort of, Gaia, but in a way also Demeter, and so on and so forth we go through the various mother-deities of Greek religion, because of how Matar/Kybele ended up refracting into all these goddesses.
