After announcing her chief of staff on Wednesday, Mrs. Trump on Thursday chose an interior designer, Tham Kannalikham, to overhaul the White House private quarters. In the coming days, she plans to announce the hiring of Natalie Jones, a former Obama administration protocol official, as her social secretary, according to people briefed on her plans, and Stephanie Winston Wolkoff, the former director of Fashion Week at Lincoln Center who planned Mr. Trump’s inaugural festivities, as her senior adviser.

“I am putting together a professional and highly experienced team, which will take time to do properly,” Mrs. Trump said in a statement on Wednesday. “I am excited to be organizing and bringing together such a dynamic and forward thinking group of individuals who will work together to make our country better for everyone.”

But for now, the lack of staff has deprived Mrs. Trump of control over her image, leading to speculation about everything from her state of mind to her moving date.

Her absence from Washington fueled rumors this week that she might never move to the capital. And with none of the customary images of the first lady adjusting to life in the White House, social media has seized instead on a meme based on video of Mrs. Trump frowning during the inauguration, spawning the hashtag #SadMelania.

Ms. Wolkoff said Mrs. Trump had every intention of moving to the White House and would be splitting her time between Washington and New York until then. “It has only been a short time since the inauguration, and the first lady is going to go about her role in a pragmatic and thoughtful way that is unique and authentic to her,” Ms. Wolkoff said.

The hiring of Ms. Reynolds appeared at least in part designed to answer concerns that have arisen about the unusually long disruption to White House tours. Ms. Reynolds said on Wednesday that she was “working to ensure that the White House Visitors Office is fully staffed and operational and ready to accept tour requests for the public in the coming weeks after a traditional temporary closure during the transition period.”