Or HaChaim on Exodus 29:46/אור החיים על שמות כ״ט:מ״ו

1 אני ה׳ אלוקיהם, "I am the Lord their G'd." The reason the Torah repeats this after having said almost the same thing in verse 45 may be to remind us that even at a time when G'd's שכינה is not manifest amongst us, He still remains our G'd. Alternatively, G'd's being truly our G'd depends on our being aware of and recognising this fact. We are only worthy of bearing His name while we recognise Him as our G'd as mentioned at the beginning of this verse. Failing this, the result will be that the people will shake off the burden of the Torah, in which event they would "belong" to other gods.