Did a little research...
From NBA.com:
The name seemingly grew out of a conversation between Brown and Howie McHugh, a member of the Garden's publicity staff and the man assigned to handle the basketball entity. Both men suggested several nicknames, including Whirlwinds, Unicorns and Olympics. But it was Brown, who suddenly exclaimed, "Wait, I've got it - the Celtics. We'll call them the Boston Celtics!" Brown excitedly went on, "The name has a great basketball tradition from the old Original Celtics in New York. And, Boston is full of Irishmen. We'll put them in green uniforms and call them the Boston Celtics!"
McHugh tried in vain to talk with, negotiate and dissuade Brown not to use the name Celtics, but Brown's mind had clearly reached a final decision and that would be the end of that conversation.
The Original Celtics were themselves an offshoot of a team called "New York Celtics", as reported on the Hall Of Fame site:
http://www.hoophall.com/halloffamers/Celtics%20Original.htm"With flair and quality fundamentals, the Original Celtics got basketball off to a new style and pace in the 1920s, bringing the pro game its first national attention. Using teenage players from Manhattan's West Side, Frank McCormack formed the team as the New York Celtics in 1914. The team disbanded during World War I, but was reformed as the Original Celtics in 1918 by promoter James Furey".
Honestly, we cannot say that the New York Celtics did or did not take the name from the Glasgow Celtic. We are deep into the realm of speculation, because only Frank McCormack could have told us the truth, but one could argue that Glasgow is in Scotland and not in Ireland... anyway, I am sure the Original Celtics (who got the name from the New York Celtics) and the Boston Celtics (who got their name from the Original Celtics) did not have their teams named after the Glasgow soccer team.
Check this site too: