In this modern age we are consistently hit with the concept of brand commitment. How will customers, or fans, be in a position to make that connection with a company or team without continuity in a name? While Green Bay has often been the Packers, not every team has always played using the name they have today.

The Chicago Bears started off as the Decatur Staleys. The Decatur Staleys? Try picturing fans these days entertaining for the mighty Decatur Staleys.

When the AFL came about in 1960 the New York team was the New York Titans. After 2 sterile seasons, the new possession modified the name to the New York Jets. Years on, Titans would resurface in the NFL when Tennessee modified its name from Oilers to Titans after moving from Houston to Nashville (with a brief stay in Memphis as the Tennessee Oilers).

In 1983, the USFL had a franchise start in Boston, Massachusetts as the Boston Breakers. In 1984 they moved to New Orleans and became the New Orleans Breakers, followed by a move in 1985 to Portland, Oregon and another name change ; this time to the Portland Breakers.

The mid-70's World Football League 's NY Stars moved to Charlotte North Carolina, played one game as the Charlotte Stars before changing their name to the Charlotte Wasps over ten years before the NBA's Charlotte Hornets came along.

The Kansas Town Chiefs have some of the most vocal and unswerving fans in the NFL, few of them were there to cheer the team when they were first called the Dallas Texans. The NFL would again bring back a formerly used AFL name when the growth Houston franchise took the name of Texans in 2002.

In the Canadian Football League the name game is also prevalent. The most intense CFL example would be the Montreal Alouettes.
The Alouettes played in the CFL from 1946 till the team ceased to be in 1981. In 1982 a new Montreal football team joined the CFL, the Montreal Concordes. 2 years after the Concordes renamed themselves the Alouettes before going into bankruptcy themselves after.
The fable of the Alouettes doesn't end there. The CFL had a transitive franchise in the North American town of Baltimore which debuted as the Baltimore Colts, and then due to litigation modified its name to the Baltimore CFL Colts and the Baltimore CFLers, before ultimately settling on the Baltimore Stallions. When the NFL asserted the Cleveland Browns would be relocating to Baltimore and becoming the Ravens, the possession of the Baltimore Stallions moved the team to Montreal and became the newest incarnation of the Montreal Alouettes.
The Arizona Cardinals were known early on as the Racine Normals, back in the time they played in Chicago.
Originally playing football as the Portsmouth Spartans, the Detroit Lions would go on to turned into one of the oldest NFL franchises. The team modified its geographic name to New England without even moving, playing their first games as the Boston Patriots. Not uncommon, the Phoenix Cardinals in a similar way became the Arizona Cardinals without moving. Due to WWII and the lack of players, the Eagles and Steelers combined for a year forming the Phil-Pitt Steagles. The Rams have been the Cleveland Rams and L. A. Rams before settling in St. Louis as the St. Louis Rams in 1995.
Though Seattle has often been the Seahawks, there had been a previous Seahawks in pro football. In 1946, the AAFC had a team called the Miami Seahawks. That year Miami was hideous off and on the field and ended up folding and going out of business. The World Football League of the 1970s had a team known as the Memphis Southmen, the franchise had originally been intended to be in Toronto and have the nickname of the Toronto Northmen.
Even the nation's Football League itself was originally named the American Pro Football organisation, or the APFA. So, truly what is in a name?