there are Youtube videos that call it that. the expanded title seems to be the correct Sanskrit name.
here is the Gita Press Ramayana
https://www.muzaffarpureshop.com/product/gita-press-shrimad-valmikiya-ramayan/
which features the full expanded name.
Yes. But there's no hard and fast rule to that effect.
But technically speaking, that's how each Sarga ends with a 'śrīmadrāmāyaṇe' in the Original Sanskrit texts, as per most resources - 1, & 2.
The ending verses of the Ayodhya Kanda, for instance goes like -
इत्यार्षे श्रीमद्रामायणे आदिकाव्ये श्रीमद्वाल्मीकीये चतुर्विंशत्सहस्रिकायाम् संहितायां श्रीमदयोध्याकाण्डे एकोनविंशत्युत्तरशततमः सर्गः
IAST
ityārṣe śrīmadrāmāyaṇe ādikāvye śrīmadvālmīkīye caturviṃśatsahasrikāyām saṃhitāyāṃ śrīmadayodhyākāṇḍe ekonaviṃśatyuttaraśatatamaḥ sargaḥ
Other Kandas too, follow the same setup.
The popular Gita Press Gorakhpur also follows the same title in their printed versions.
The much older Hindi translation rendition by Chaturvedi Shri Dwarka Prasad "Sharma" aka DP Sharma too, also prints it as - 'śrīmad-vālmīkī-rāmāyaṇa' and same sanskrit verses in their prints.
So, yes. The expanded title "technically" seems to be one of the correct Sanskrit titles for the work by Maharshi Valmiki.
There is nothing improper in calling Valmiki Ramayana as Shrimad Valmikiya Ramayana. Both the names are correct.
We add 'Shri' or 'Shrimad' etc. before a word for giving respect. Like for example, we say Shrimad Bhagvata Purana, instead of simply calling it as Bhagvata Purana or we say Shrimad Adishankaracharya instead of calling him just by his name.
Both words are correct in above examples.
'Srimad' (or 'Srimat', Sanskrit श्रीमत्) means 'radiant', 'holy', 'splendid', or 'glorious',[28] and is an honorific religious title.
And for the second part of your question that the expanded title seems to be the correct sanskrit name, Again, it's nothing like this. There are even many names of the Valmiki Ramayanam itself.
That sage with observed sacred vows has rendered the entire epic in the name of 'Ramayana', 'Sublime Legend of Seetha' and 'elimination of Ravana'. [1-4-7]
Sources used:
http://www.valmikiramayan.net/bala/sarga4/balaitrans4.htm#Verse7
