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Design a 3-bit counter using D-flip flops such that not more than one flip-flop changes state between any two consecutive states.
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Can we use Johnson Counter here??
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Yes.

State diagram will be as  (remember concept of gray code)

State table and $3-bit$ synchronous counter with D FFs, will be as

$\begin{array}{c|c|c} \text{Present State}&\text{Next State}&\text{FF Inputs}\\\hline ABC&\bar A \bar B \bar C & D_AD_BD_C\\\hline 001&011&011\\000&001&001\\010&110&110\\011&110&110\\100&000&000\\101&100&100\\110&111&111\\ \end{array}$

$D_{a}= AC+B\bar{C}$
$D_{b}= \bar{A}C+B\bar{C}$
$D_{c}= \bar{A}\bar{B}+AB=A\odot B$

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a johnson counter would also count the same
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@Tushar, But Johnson's counter can count only 6 states with 3 flipflops(3 bits output), right? how can it count the same?
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oh yeah i had got that now  @chauhansunil20th thanks for pointing out

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We count in Gray Code :

Present  state       Next state
Q2 Q1 Q0 D2 D1 D0 Q2 Q1 Q0
0 0 0 0 0 1 0 0 1
0 0 1 0 1 1 0 1 1
0 1 1 0 1 0 0 1 0
0 1 0 1 1 0 1 1 0
1 1 0 1 1 1 1 1 1
1 1 1 1 0 1 1 0 1
1 0 1 1 0 0 1 0 0
1 0 0 0 0 0 0 0 0

D2=Q1Q0'+Q2Q0

D1=Q2'Q1+Q1Q0'

D0=Q2'Q1'+Q2Q1

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I am getting

D2= Q1Q0' + Q2Q0

D1= Q2'Q0 + Q1Q0'

D0= Q2'Q1' + Q2Q1. Could you please check?
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how to get Do,D1,D2 coloum pllzzz explain

use gray code for 1 bit change

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