They are many interesting hurdles one comes up against when one has syncretic worship from two (and for some folks it can be more) cultures. This is on top of modern adaptations that come with ones worship, such as the fact that as someone who religiously follows a lunar calendar and follows a solar calendar too this means that I not only have my traditional oikos holy days, but also days that I consider sacred to certain gods in the solar week. Now when you are blending two cultures this can get complicated because each culture has their own sacred days ascribed for various reasons. This came up in a conversation for me today, because as a Hellenic and Hindu syncretist I tend to observe worship for Apollon and Helios/Surya on Sundays (unlike a typical calendar I consider Sunday the weekEND and that the new week really doesn’t begin until Monday, therefore making Sunday the 7th day in the week and also appropriate for Apollon in that respect) and Mondays for Shiva. It was mentioned that one could just honor them both on one day (presumably towards one primary religious expression and worship) but I don’t agree with this. I am syncretic but there are reasons and symbols behind each sacred action and occasion. However, I do address Shiva’s name in my prayers to Apollon on Sunday and Apollon’s name in the prayers to Shiva on Monday, which would also be appropriate for addressing Apollon at the beginning of the new week as he is addressed at the beginning of the new lunar month. So while this gives me a bit of extra work, it is by no means objectionable to me. Naturally, because I observe both days the tone of each will be a bit different…such as that I do fast on Monday but not on Sunday. Of course Mondays are also sacred to Leto and Selene in my household, which means I am usually doing other offerings and prayers in addition.
Wednesdays are typically for Hermes, and although Ganesh is honored with Shiva and Paravati on Monday, I also honor Ganesh on this day with with his Hellenic form as Hermes as he doesn’t have a specifically ascribed sacred day in the week. Thursdays meanwhile are all for Zeus and Hera, it also the day for honoring Vishnu (whom I syncretically associate with Zeus), though in some places Vishnu is also honored on Wednesdays additionally. Friday is in honor of Durga and Kali, and I tend to honor Aphrodite and Ares on Friday. Meanwhile Rhea (who I consider to be the same as Durga) and Artemis (who I associate with Paravati and Kali) I also honor on Saturday.
Of course this is always a work in progress in building my religious calendar, and I am slow to add Hindu gods as it is taking some time to become a bit familiar with them. I don’t have a weekly observance for Athena as you notice, even though she is a goddess of my household, but I do honor her on her domestic rites in the lunar calendar of the oikos and with her I honor Saraswati who I consider to be her Hindu manifestation. Surprisingly although it is complicated having gods that I synretically link honored on differing days and in their own particular cultural customs, I make a point to acknowledge the other manifestation from the other culture on whatever day I am observing.