Or talīmātu. No definitive etymology can be suggested. An eventual connection to talīmu ''brother' is possible.
See also talīmtu '(beloved) sister' (AHw 1310, CAD T 94). The origin of the Akkadian word is uncertain. It is clearly unseparable from JPA tlym 'twin brother', and Sam. tlym 'brother', but the background of their relationship is not easy to evaluate: while AHw 1310 and Krispijn 2001, 255 do not hesitate to treat the Aramaic words as Akkadisms, Kaufman 1974, 106 believes that “the forms are probably cognate”. Kaufman’s doubts must be due to the reasonable (even if not pronounced) observation that exclusive Akkadisms are not very likely to appear in manifestly Western Aramaic varieties such as JPA and Samaritan. Kaufman hypothesises that talīmu may have originated as a taC1C2īC3-derivate from PS *lˀm. This etymology is not without appeal both semantically and formally (cf. GAG §56l for other Personbezeichnungen formed after this pattern). Arb. at-tilmu = al-ġulāmu ‘boy, servant’ (LA 12 76), apparently also considered an Akkadism (or Aramaism of an eventually Akkadian background) by von Soden, is semantically rather remote for a loan relationship, but perhaps suitable as a cognate.
Perhaps borrowed from Sum. dal.dal, which, however, does not seem to be attested beyond the lexical list Hh III 406 as an equivalent of the Akkadian word. Landsberger 1967b, 19 further hypothesizes an eventual derivation from dal(.dal) “to fly”, presumably referring to particles of pollen “flying” in the air. It seems resonable to agree with Landsberger 1967b, 1 that Akk. taltallu and Hbr. taltallīm (HALOT 1741, hapex in Canticle 5:11) are etymologically unrelated (see the discussion in EDA II). More promising is Arb. taltalat- 'a drinking-vessel that is made of the envelope of the spadix of a palm tree', for which the connection to the date palm is explicitly preserved in the tradition. If indeed related to the Akkadian word, the Arabic term might point to an eventual Semitic origin of the latter, in which case Sum. dal.dal must be an Akkadism.
The origin of the Akkadian word is unclear. It is thought to be borrowed into South Mesopotamian Middle Aramaic varieties (von Soden in AHw. 1312, but not in Kaufman 1974): JBA tālətā 'species of date palm', Mnd. tala 'young date-palm'. From there, it may have penetrated into Arabic as tāl- 'young date-palms, palm saplings', also attested in the modern dialects of Iraq. For Sab. tl ‘young palms’ see Sima 2000, 249–250 who does not make explicit his understanding of the diachrony of the Sabaic word (an Aramaism in Sabaic is not so easy to surmise). As seen already by Löw 1881, 112, the Semitic words under scrutiny come notoriously close to Sanskrit tālaḥ ‘Weinpalme’ (KEWA 498). Contra Sima’s hypercritical evaluation (2000, 249), this similarity can by no means be accidental. Mayrhofer does not hesitate to treat all Semitic forms (inlcuding Akkadian) as Indian loanwords, which is rather problematic in view of the early (OB) attestation of Akk. tālu. Note that in Mayrhofer’s view the Sanskrit word has no convincing IE etymology and may have a Dravidian origin.
Reliable attestations are from later periods, which points to a WS borrowing.