Sri PiLLailOkam Jeeyar in his taniyan vyaakyaanam explains well, how it can be taken that Sri AaNdaaL had Periya PerumaaL in her mind. From her Naacchiyaar Tirumozhi and Tiruppaavai, one can see that she associated Tiruvaranganaar with Sri Varaahap PerumaaL (as she is Bhoomi piraatti's amsam she recalls His help in the past) and Sri Krishnar (whom she relates to as an idaippeN). She also sings about waking up the resting Lord and that is also to be looked at as Sri Ranganathar. TiruppaaNaazhvaar also sings about Periya PerumAL as "kOvalanAi veNNai uNda vaayan".
It is clear that Sri AaNdaaL definitely had Sri Ranganathar in mind when composing Tiruppaavai.
So, why did she not mention His name in the 30 verses? I like Sri Sudarshan's note that she was being shy, as the to-be-bride of Sri Ranganathar, and keeping with the decorum of the time would not directly mention her groom's name. It would also make sense from those times that she would refer to Him through other names but not His direct name.
Adiyen also thinks the following: as has been mentioned before, Sri AaNdaaL wrote Tiruppaavai as an idaippeN. Our aachaaryas have noted that no where does she use words related to her upbringing and instead uses words and phrases entirely related to yaadava girls.
The extent of Sri AaNdaaL's transformation into a yadava girl is thus noted by our aachaaryas. When Maarican took the form of a golden deer, it is said that all the animals in the forest shyed away from him as he still could not hide his raakshasa gantham. Our EmperumAn however hid His iishvarathvam when He took different forms (Sri AaNdaaL writes "maanamillA panRi" in Naacchiyaar Tirumozhi). Our piraatti even excelled Him in this regard, by taking on a different personality completely while already being born in this world in Sri Periyaazhvaar's household.
As an yaadava girl it would have been out of place to write about the archaavataaram of Sri Ranganathar directly, even though she had Him in mind.
The amazing thing, thus, is that whereas many have seen vibhavaataaram of Sri Krishna in Periya PerumaaL, Sri AaNdaaL saw the archaavataaram of Sri Ranganathar in Sri Krishnar. Sri ManavALa Mamunigal aptly says, "aazhvaargaL tham seyalai vinji niRkum thanmaiyaLaay".