The names of the male Brandybucks are generally derived from Old Welsh. The name Meriadoc seems to mean something like 'great one', an interpretation that is uncertain, but matches well with his sobriquet of 'the Magnificent'.
We're given practically no information about the progeny or descendants of Meriadoc and Estella, but we can be sure that they had at least one son. In Appendix B to The Lord of the Rings, in the entry for Shire Year1484, Merry and Pippin '...handed over their goods and offices to their sons'. We know from other sources that the son of Peregrin mentioned here was named Faramir, but there is no comparable reference to Meriadoc's heir.