Their sorrows shall be multiplied that hasten after another god. This is the only note of sadness in the entire psalm, and it is inserted to add force by contrast to the joyous outburst in Psalms 16:5.
If men would not cleave to Jehovah, but would "hasten after"—or perhaps it should be translated "wed themselves to"—another god (see Exodus 2:16, the only other place where the word occurs), then they must not expect "prosperity," or joy of any kind.
Their "sorrows will be multiplied;" distress and anguish will come upon them (Proverbs 1:27); they will have to pay dear for their apostasy. Their drink offerings of blood will I not offer. Drink offerings of actual blood are not elsewhere mentioned in Scripture, and there is very little evidence of their having been offered by any of the heathen nations, though it is conjectured that they may have been employed in the worship of Moloch.
It is therefore best to explain the expression, as hero used, metaphorically, as drink offerings as hateful as if they had been of blood (comp. Isaiah 66:3). Nor take up their names into my lips. By "their names" we must understand the names which they used—those by which they called their gods.
The Law forbade the mention of these names by Israelites (Exodus 23:13; Deuteronomy 12:3).