1 syllable:
aim, aimbe, aime, ame, baim, bame, blame, bleyme, boehm, boehme, brame, came, chame, claim, crame, dame, damme, fame, fayme, fe mm, flaim, flame, fraim, frame, game, graeme, grame, haim, kaim, lame, maamme, maim, mame, mayme, name, payme, prame, rhame, rtgame, same, scame, sejm, shame, sname, swaim, tame, trame

2 syllables:
a-frame, aa mm, acclaim, aflame, agame, agname, airframe, arkaim, ashame, ballgame, ball game, became, bedframe, beldame, big-name, big game, birthname, boardgame, board game, brand-name, brandname, by-name, byname, card game, chess game, child's game, code-name, coldframe, cold frame, con game, court game, crap game, cross-claim, dagame, day game, declaim, defame, diblaim, diffame, disblame, disclaim, disclame, disfame, doorframe, dulaim, efraim, eglaim, ename, enflame, enframe, entame, essaim, exclaim, fair game, false name, fangame, field game, filename, first-name, first name, foregame, freeze-frame, gameframe, golf game, goodgame, go game, grandame, grande dame, hangame, headframe, head game, hogframe, home game, hutaym, icame, iframe, igname, ill fame, iname, inflame, in name, keyframe, khadgam, last name, lay claim, lovegame, mainframe, make-game, matched game, match game, mazame, misclaim, misframe, misname, mizraim, moorgame, nachname, nandaime, nickname, night game, no-name, noname, nonclaim, nongame, ogame, part name, pathname, pay claim, pen-name, pen name, philem, place-name, place name, playgame, postgame, pregame, prename, proclaim, pygame, quiname, quitclaim, r.a.m, rakeshame, re-claim, reclaim, reflame, reframe, reklame, rename, rephaim, road game, schooldame, self-same, selfsame, shell game, sirname, soname, spaceclaim, sports game, stage name, stealth game, stepdame, sub-frame, subframe, subgame, surname, take aim, tannaim, the same, timeframe, to-name, trade name, two-name, uname, unframe, vidame, vorname, wage claim, war-game, warframe, wargame, war game, wegame, whole name, wireframe, word game, ysame

3 syllables:
abel-maim, acesulfame, action game, adoraim, advergame, aftergame, all the same, amoraim, apodeme, arcade game, aspartame, assumed name, author's name, away game, banking game, baseball game, basename, bloody shame, browser game, burlingame, call-by-name, candle flame, chinese name, christian name, cname, codename, counter-claim, counterclaim, cover-shame, darwin's game, dateiname, disinflame, domain name, doppelname, dragonframe, edamame, ekename, ender's game, eurogame, fireflame, first they came ..., forename, gacha game, given name, guessing game, hall of fame, hippodame, hockey game, horonaim, indie game, initgame, khaby lame, kirjathaim, lanciname, laying claim, maiden name, manner name, megagame, middlegame, minigame, misbecame, molly's game, neotame, numbers game, open frame, oriflame, outdoor game, overcame, overname, parlor game, party game, passing game, perfect game, picture frame, pinball game, placename, playoff game, poker game, practice game, proper name, racing game, running game, samegame, sayhername, sense of shame, sepharvaim, set aflame, sitename, softball game, spinning frame, stickball game, superframe, table game, tokoname, tradename, truename, underframe, username, waiting game, whatshisname, whatsisname, window frame, without aim, writer's name

4 syllables:
abel-mizraim, amerigame, athletic game, baptismal name, basketball game, beheading game, body-on-frame, chinese surname, company name, computer game, confidence game, dinosaur game, family name, gambling game, inertial frame, insurance claim, japanese name, one and the same, reference frame, role-playing game, survival game, the grand tour game, videogame, video game, volleyball game

5 syllables:
aram-naharaim, a horse with no name, battle royale game, chushan-rishathaim, embroidery frame, exhibition game, sports video game, wansapanataym

6 syllables:
action-adventure game, action role-playing game, by any other name, hollywood walk of fame, new york mets hall of fame, puzzle video game, racing video game, rock and roll hall of fame, the imitation game, wwe hall of fame

7 syllables:
inertial reference frame, list of birds by common name, list of plants by common name, pathfinder roleplaying game, role-playing video game, strategy video game, the hunchback of notre-dame

8 syllables:
multi-player video game, multiplayer video game, simulation video game, single-player video game