A company created by Michael Cohen, President Donald Trump’s personal lawyer, received $500,000 in 2017 from an investment fund linked to a Russian oligarch, according to a person familiar with the matter.

Separately, AT&T Inc. said it made payments to Mr. Cohen’s company in 2017 for “insights” into the administration at a time when the telecommunications giant needed government approval for an $85 billion takeover of Time Warner Inc.

The...