That last line is an important clue. "Their fathers forgot my name for Baal" would mean "they were worshipping Baal instead of me".
Now we know that these prophets were claiming to be prophets of the Lord, because they "prophesy lies in my name" (v25). How, then, would they be diminishing his worship? I suggest they were doing it by tolerating the common practice of combining the worship of the Lord with the worship of other gods. Other passages from Jeremiah and Ezekiel show that this was happening at the time.In Jeremiah ch7, offerings were being made in Jerusalem to the "Queen of heaven", apparently at the same time that men were coming up to "worship the Lord" (v1), and very probably by the same people. In Ezekiel ch14, the Lord refuses to speak to "certain of the elders" who have come to consult Ezekiel, because he knows that "these men have taken their idols into their hearts and set the stumbling-block of their iniquity before their faces" (Ezekiel ch14 v2, RSV). They are paying their respects to at least two deities at the same time.
Jermiah and Ezekiel are consistently teaching that the Lord will judge the nation for its idolatry. The false prophets are ignoring this teaching and promising the continuing favour of the Lord. Like those in ch27 v16, and Hananiah in ch28, who are prophesying that the sacred vessels lately seized by the Babylonians will soon return when the Babylonians are defeated. They implicitly, at least, encourage the idolatry of the people, by telling them that their idolatry will have no consequences. They "lead my people astray by their lies and their recklessness" (v32).
The "name" of the Lord includes his prestige and reputation. His position as the exclusive God of Israel is part of his name. If his people are sharing their time with other gods, then they are forgetting his name.