Not that I know of, but my dad had a close one, 7 letter word, negated.
dad IS a 3 letter word for dad...... Pop is another which is an abbreviation for papa .
Sire
POPS
pater
tup
dad
dead dad
'rents
dad
dad, end, read, crossword, head, lead, band, bended, bend, bed, . . . . .
3-letter words beginning and ending with the same letter: * bib * bob, Bob * dad * did * dud * eye * ewe * ere * eve * gag * gig * huh * mam * mom * mum * Nan * non * nun * pap * pep * pip * pop * pup * sis * tot * tat * tit * wow