I see what your partner is getting at! It’s the same reason one might name their child [name_f]Delilah[/name_f], or [name_f]Lilith[/name_f]. I mean, people name their sons [name_m]Apollo[/name_m] and think of all the horrific things the god [name_m]Apollo[/name_m] did. 
For me personally, the meaning is not inappropriate or off-limits as it refers to the mythological siren, but objectively, the sound/look of the world itself is off-putting. As another poster said, it puts one to mind of sirens that go off in an emergency. Average joes who hear your daughters name and aren’t well-versed in mythology will probably think of that, and honestly - I thought of the scary monster Sirenhead 
But as for what your partner is getting at, I’m all for it. There are good and bad associations with basically any character in any mythology. Many people name their sons [name_m]David[/name_m], and the Biblical [name_m]David[/name_m] killed [name_f]Bathsheba[/name_f]'s husband because he wanted her for himself. Does that mean [name_m]David[/name_m] is a bad name? Evidently not.
With all that being said, the word siren has evolved over time away from the mermaid association into just “seductress” which might be missing the mark he’s going for.
You might try these alternatives for Siren which still reference the mythological siren and/or evoke a luminous, deep-sea, man-eating mermaid 
[name_f]Sirene[/name_f] (simply putting an e on the end makes it much more beautiful and name-like, and instantly does away with the wee-ow-wee-ow association)
[name_f]Sirena[/name_f]
[name_f]Serena[/name_f]
[name_u]Seren[/name_u] (meaning ‘star’ in Welsh)
[name_f]Serene[/name_f]
[name_f]Selene[/name_f] (mythological goddess of the moon)
[name_f]Selena[/name_f]
Syrene
[name_f]Syrena[/name_f]
Mermaid/siren names:
[name_f]Sereia[/name_f] (Spanish, meaning ‘mermaid’)
[name_f]Allura[/name_f] (alluring)
Ephyra (‘daughter of [name_m]Oceanus[/name_m]’)
Assana (Irish, meaning ‘waterfall’)
[name_f]Vanora[/name_f] (Irish, ‘white wave’)
[name_f]Lumina[/name_f]
[name_f]Nerine[/name_f]/Nerina (Greek, ‘nymph of the sea’
Aquamarine
Esmerine
[name_f]Meris[/name_f]/Merise/Merissa (Latin American, ‘of the sea’)
[name_f]Morwenna[/name_f] (Welsh, ‘sea wave’)
[name_f]Morgana[/name_f] (Celtic, ‘dweller of the sea’)
[name_f]Ondine[/name_f] ([name_u]French[/name_u], ‘wave of water’)
[name_f]Thalassa[/name_f]
[name_f]Nerissa[/name_f] (Latin American/Greek ‘daughter of the sea/nymph of the sea’
[name_f]Naia[/name_f] (Hawaiian, ‘to flow’)
[name_f]Melusine[/name_f]
[name_f]Marina[/name_f]/Marinella/Marine
[name_f]Lorelai[/name_f]
[name_f]Laguna[/name_f]
[name_f]Nereida[/name_f]/Nerida
[name_f]Cyrene[/name_f]
Odyssea
Word names that evoke the sea, mermaids and myth:
[name_u]Tempest[/name_u]
[name_f]Treasure[/name_f]
[name_u]Storm[/name_u]
[name_f]Cascade[/name_f]
[name_f]Pearl[/name_f]
[name_f]Opal[/name_f]
[name_u]Ocean[/name_u]/Oceane/Oceana
[name_u]Lyric[/name_u]
[name_f]Delta[/name_f]
[name_f]Aura[/name_f]
[name_f]Jewel[/name_f]
[name_f]Lullaby[/name_f]
[name_u]Echo[/name_u]
[name_f]Aqua[/name_f]
[name_u]River[/name_u]
[name_u]Rain[/name_u]
[name_u]Onyx[/name_u]