There is a definite difference between Taylor and Tyler, although Taylor tends towards Tyler, and Tyler tends toward Toyler.
This is a feature most marked in 'broad' Australian.
The IPA phonological representation is still /eI/, but the initial /e/ of the diphthong is more open and centralised.
"The glides in the HOWD and HODE vowels have different orientations in RP relative to AusE and the HADE, HIDE, HOYD vowels have undergone a process of shift such that AusE HADE is similar to RP HIDE and AusE HIDE is similar to RP HOYD. These differences may in some instances lead to misunderstanding such as the unfortunate woman who believed she was being sent home from the hospital ‘to die’ after being informed that she was ‘going home today’.
http://clas.mq.edu.au/felicity/Papers/OZWORDS.pdf
Here's a phonetic dipthong chart for AusE.
Australian dipththongs
Even though we might speak this way, if your name is Taylor, it is
not advisable to tell an Aussie your name is Tyler in the hope that they will recognise it as Taylor.