The word 'Saraswati' has several meanings:
सरस्वती 1 N. of the goddess of speech and learning, and represented as the wife of Brahman and often of Vishnu; परस्पर- विरोधिन्योरेकसंश्रयदुर्लभम् । संगतं श्रीसरस्वत्योर्भूतये$स्तु सदा सताम् ॥ V.5.24. -2 Speech, voice, words; इति देहविमुक्तये स्थितां रतिमाकाशभवा सरस्वती ... अन्वकम्पयत् Ku.4.39,43; R. 15.46. -3 N. of a river (which is lost in the sands of the great desert). -4 A river in general. -5 A cow; ŚB. on MS.1.3.49; Vāj.8.43. -6 An excellent woman. -7 N. of Durgā. -8 N. of a female divinity peculiar to the Buddhists. -9 The Soma plant. -1 The plant called ज्योतिष्मती-10 speech or the power of speech, eloquence, learning wisdom
The Rig-Veda describes Sarasvati as Devi :
Paavakaa Nah Sarasvatii Vaajebhir-Vaajiniivatii |
Yajnyam Vassttu Dhiyaavasuh ||1.3.10||
Meaning : O Saraswati, You are the purifier (of our Intellect), and Your Strength (of Wisdom) grows within us with Sacrificial Offerings (inner and outer),May my offering in Yagnya strengthen Your Wisdom within me (i.e. May Your presence within me make me rich in Wisdom).
It also described Sarasvati as river :
Maho Arnnah Sarasvatii Pra Cetayati Ketunaa |
Dhiyo Vishvaa Vi Raajati ||1.3.12||
Meaning : Saraswati, that Great Wave (of Universal Wisdom) (Who has flowed as a River) and Who is the awakener of our Intellect, is (now) shining as the embodiment of Universal Wisdom (in this Yagnya).
Regarding the SECOND meaning, the derivation is shown as : -/sri (सृ)+ asun (असुन्)= saras (सरस्) meaning 'watery substance' + vati (वती ie वतुप् स्त्री) meaning 'containing of' = sarasvati. Monier Williams mentions however that we have to take saras as 'Speech' to get the meaning of 'Sarasvati' as Devi as She is the Deity of Speech.
We must remember that the grammatical meaning involving 'saras' and therefore implying a river evolved much after than the word already used in the Rig-Veda.We therefore must accept both the meanings simultaneously, as the grammatical derivations result from Panini's works which are composed many hundred (if not thousands) years after the Rig-Veda was compiled.
Reference : https://www.sanskritdictionary.com/?iencoding=iast&q=%E0%A4%B8%E0%A4%B0%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%A4%E0%A5%80&lang=sans&action=Search and http://greenmesg.org/stotras/saraswati/saraswati_mantras.php