Although born in Voskresensk, Namestnikov moved to the United States when he was eight months old, settling in Salt Lake City, Utah, with his family. When he was eight, he returned to Voskresensk in Russia to hone his hockey skills, eventually playing in the Vysshaya Liga with Khimik Voskresensk at the age of 16. He was eventually picked by the London Knights 20th overall in the 2010 Ontario Hockey League (OHL) entry draft, and was also selected 11th overall in the Kontinental Hockey League (KHL) draft by Torpedo Nizhny Novgorod, but said, "I'm not going back there [Russia] to play."
On 13 March 2012, the Tampa Bay Lightning announced the signing of forward Namestnikov to a three-year, entry-level contract. He played in 60 games with the London Knights that season, scoring 22 goals and 70 points to go along with 60 penalty minutes. In his career with the Knights, he has skated in 128 career games over the past two seasons, registering 52 goals and 139 points, and a +29 rating. Namestnikov appeared in six OHL playoff games last year, recording one goal and five points.
On 14 September 2012, the Lightning assigned Namestnikov and 17 other players to the Syracuse Crunch, their American Hockey League (AHL) affiliate, during the 2012–13 NHL lockout. On 21 October, Namestnikov suffered a shoulder injury when he slammed into the boards with a Wilkes-Barre/Scranton Penguins player in the first period. The team revealed that Namestnikov was expected to miss four-to-six weeks with the injury. He finished the season playing in the Calder Cup Final, where the Crunch fell to the Grand Rapids Griffins in a 4–2 series defeat.
On 23 November 2013, Namestnikov suffered a broken hand against the Hamilton Bulldogs during the third period of the game when he took a shot off of his hand. On 7 February 2014, Tampa Bay recalled Namestinkov from the Crunch. At the time, he skated in 31 games this season with Syracuse, posting 13 goals and 30 points to go along with 19 penalty minutes. He ranked tied for first on the team for points and assists. Namestnikov made his NHL debut on 8 February 2014, skating 11:55 for the Lightning in their 4–2 win over the Detroit Red Wings. On 5 March 2014, Namestnikov was reassigned to the Crunch after appearing in four NHL games, though failing to record a point. He set career-high totals for games played (56), goals (19), assists (29), points (48) and penalty minutes (40) during the 2013–14 season in the AHL with Syracuse.
On 6 January 2015, Namestnikov was named an AHL All-Star, representing the Eastern Conference. On 21 January 2015, he was named into the starting lineup. At the time of the announcement, he had eight goals and ten assists for 18 points in 18 games.
Namestnikov made the Tampa Bay opening night roster out of training camp to start the 2014–15 season. On 13 October 2014, he picked up his career first NHL assist and point on a Victor Hedman goal, as well as his first NHL goal, in a 7–1 victory over the Montreal Canadiens. He then scored his first game-winning goal on 24 October against the Winnipeg Jets. On 3 December 2014, the Lightning reassigned Namestnikov to Syracuse. The move was done to give him more playing time and he would also be playing in his natural position, center. The move also freed-up some room for Tampa's highly touted teammate Jonathan Drouin to receive more ice time; Drouin and Namestnikov had been alternating healthy scratches for the team, playing as the third-line left wing on a rotational basis. On 4 March 2015, the Tampa Bay Lightning recalled Namestnikov from Syracuse. In 26 games with the Lightning this season, Namestnikov has recorded three goals and seven points with a plus-3 rating. On 28 March, the Lightning elected to keep Namestnikov for the playoffs by using one of their two remaining call ups. Namestnikov had previously been on an emergency recall, however, his strong play made the teams choice easy with his strong play since being recalled. On 30 March 2015, in a Tampa Bay Lightning 5–3 win over the Montreal Canadiens, Namestnikov scored two goals, including the game winner, which helped the lightning clinch a playoff berth in the 2014–15 NHL Playoffs. During this game he also had an assist, along with the game-best possession stats (14 shot attempts for, 6 against, 70.0%).Namestnikov also has seven points (4g, 3a) in the past seven games.
On 17 July 2015, the Lightning announced the re-signing of Namestnikov to a one-year, two-way contract. Namestnikov skated in 43 games with the Lightning during the 2014–15 NHL season, posting nine goals and 16 points (9–7–16), which were all career highs. Namestnikov appeared in 12 Stanley Cup playoff games in 2015, recording one assist. In addition, he played in 34 games with the Syracuse Crunch during the 2014–15 season, registering 14 goals and 35 points.
On 15 January 2016, Namestnikov recorded his first career NHL hat trick in a 5–4 overtime win over the visiting Pittsburgh Penguins at Amalie Arena. On 3 May 2016, Namestnikov recorded his first NHL playoff goal, which came in a 5–4 overtime Lightning win over the New York Islanders.
He re-signed a two-year, $3.875M deal with the Lightning during summer 2016.
On 2 March 2016, the Russian Ice Hockey Federation named Namestnikov to its roster for the 2016 World Cup of Hockey. Namestnikov was joined by Lightning teammates Nikita Kucherov, Nikita Nesterov and Andrei Vasilevskiy. The tournament took place from 17 Sep to 1 October 2016, in Toronto. On May 21, 2017, Namestnikov helped Russia capture a bronze medal when they defeated Finland in the bronze medal game.
Namestnikov's father, Evgeny, was a player for the Vancouver Canucks and also played for Torpedo Nizhny Novgorod. His uncle on his mother's side is Vyacheslav Kozlov, a former NHL star having played in over 1,000 games in the NHL for the Detroit Red Wings, Buffalo Sabres and Atlanta Thrashers, playing on a line with current Lightning general manager Steve Yzerman with Detroit. Another uncle, Ivan Novoseltsev, is also a hockey player, having played over five seasons in the NHL and currently playing in Russia. His family emigrated to the United States in 1993 when Vladislav was eight months old, initially arriving in Salt Lake City, Utah.
On 18 November 2014, the Tonight Show with Jimmy Fallon did a segment on the possible expansion of the NHL to Las Vegas. During the segment, the program listed the pros and cons of the city getting a team. On one of the pro's section, Fallon joked about getting to "see names like Semyon Varlamov, Vladislav Namestnikov and Alexei Ponikarovsky." To his credit, Fallon was able to pronounce Namestnikov's name correctly.