I would have made (fact_id, name_id) into a two-column primary key:

fact_id fact
------- ----------------------
1       foo is a fooity foo
2       bar is a barrish baaar

fact_id name_id name
------- ------- -------
1       1       foo
1       2       foog
2       1       bar
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Then you could always find the primary name out by querying WHERE fact_id = ? AND name_id = 1.